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p",[569,1092,1094,1112,1130],{"className":1093,"ariaHidden":599},[598],[569,1095,1097,1100,1103,1106,1109],{"className":1096},[603],[569,1098],{"className":1099,"style":672},[607],[569,1101,696],{"className":1102},[612,613],[569,1104],{"className":1105,"style":796},[723],[569,1107,700],{"className":1108},[800],[569,1110],{"className":1111,"style":796},[723],[569,1113,1115,1118,1121,1124,1127],{"className":1114},[603],[569,1116],{"className":1117,"style":841},[607],[569,1119,630],{"className":1120},[612,613],[569,1122],{"className":1123,"style":848},[723],[569,1125,719],{"className":1126},[852],[569,1128],{"className":1129,"style":848},[723],[569,1131,1133,1136],{"className":1132},[603],[569,1134],{"className":1135,"style":672},[607],[569,1137,565],{"className":1138},[612,613]," ist anschaulich: Bei ",[569,1141,1143,1156],{"className":1142},[572],[569,1144,1146],{"className":1145},[576],[578,1147,1148],{"xmlns":580},[582,1149,1150,1154],{},[585,1151,1152],{},[588,1153,630],{},[592,1155,630],{"encoding":594},[569,1157,1159],{"className":1158,"ariaHidden":599},[598],[569,1160,1162,1165],{"className":1161},[603],[569,1163],{"className":1164,"style":642},[607],[569,1166,630],{"className":1167},[612,613]," Versuchen mit je Trefferwahrscheinlichkeit ",[569,1170,1172,1185],{"className":1171},[572],[569,1173,1175],{"className":1174},[576],[578,1176,1177],{"xmlns":580},[582,1178,1179,1183],{},[585,1180,1181],{},[588,1182,565],{},[592,1184,565],{"encoding":594},[569,1186,1188],{"className":1187,"ariaHidden":599},[598],[569,1189,1191,1194],{"className":1190},[603],[569,1192],{"className":1193,"style":672},[607],[569,1195,565],{"className":1196},[612,613]," erwartet man im Mittel ",[569,1199,1201,1219],{"className":1200},[572],[569,1202,1204],{"className":1203},[576],[578,1205,1206],{"xmlns":580},[582,1207,1208,1216],{},[585,1209,1210,1212,1214],{},[588,1211,630],{},[698,1213,719],{},[588,1215,565],{},[592,1217,1218],{"encoding":594},"n \\cdot p",[569,1220,1222,1240],{"className":1221,"ariaHidden":599},[598],[569,1223,1225,1228,1231,1234,1237],{"className":1224},[603],[569,1226],{"className":1227,"style":841},[607],[569,1229,630],{"className":1230},[612,613],[569,1232],{"className":1233,"style":848},[723],[569,1235,719],{"className":1236},[852],[569,1238],{"className":1239,"style":848},[723],[569,1241,1243,1246],{"className":1242},[603],[569,1244],{"className":1245,"style":672},[607],[569,1247,565],{"className":1248},[612,613]," Treffer. ",[569,1251,1253,1267],{"className":1252},[572],[569,1254,1256],{"className":1255},[576],[578,1257,1258],{"xmlns":580},[582,1259,1260,1264],{},[585,1261,1262],{},[588,1263,696],{},[592,1265,1266],{"encoding":594},"\\mu",[569,1268,1270],{"className":1269,"ariaHidden":599},[598],[569,1271,1273,1276],{"className":1272},[603],[569,1274],{"className":1275,"style":672},[607],[569,1277,696],{"className":1278},[612,613]," muss keine ganze Zahl sein.",[565,1281,1282,1311,1312,1340,1341,1369,1370,1400,1401,1429,1430,1495],{},[569,1283,1285,1299],{"className":1284},[572],[569,1286,1288],{"className":1287},[576],[578,1289,1290],{"xmlns":580},[582,1291,1292,1296],{},[585,1293,1294],{},[588,1295,762],{},[592,1297,1298],{"encoding":594},"\\sigma",[569,1300,1302],{"className":1301,"ariaHidden":599},[598],[569,1303,1305,1308],{"className":1304},[603],[569,1306],{"className":1307,"style":642},[607],[569,1309,762],{"className":1310,"style":966},[612,613]," beschreibt, wie weit die Trefferzahl typischerweise von ",[569,1313,1315,1328],{"className":1314},[572],[569,1316,1318],{"className":1317},[576],[578,1319,1320],{"xmlns":580},[582,1321,1322,1326],{},[585,1323,1324],{},[588,1325,696],{},[592,1327,1266],{"encoding":594},[569,1329,1331],{"className":1330,"ariaHidden":599},[598],[569,1332,1334,1337],{"className":1333},[603],[569,1335],{"className":1336,"style":672},[607],[569,1338,696],{"className":1339},[612,613]," abweicht. Für ",[569,1342,1344,1357],{"className":1343},[572],[569,1345,1347],{"className":1346},[576],[578,1348,1349],{"xmlns":580},[582,1350,1351,1355],{},[585,1352,1353],{},[588,1354,565],{},[592,1356,565],{"encoding":594},[569,1358,1360],{"className":1359,"ariaHidden":599},[598],[569,1361,1363,1366],{"className":1362},[603],[569,1364],{"className":1365,"style":672},[607],[569,1367,565],{"className":1368},[612,613]," nahe ",[569,1371,1373,1387],{"className":1372},[572],[569,1374,1376],{"className":1375},[576],[578,1377,1378],{"xmlns":580},[582,1379,1380,1385],{},[585,1381,1382],{},[748,1383,1384],{},"0",[592,1386,1384],{"encoding":594},[569,1388,1390],{"className":1389,"ariaHidden":599},[598],[569,1391,1393,1397],{"className":1392},[603],[569,1394],{"className":1395,"style":1396},[607],"height:0.6444em;",[569,1398,1384],{"className":1399},[612]," oder ",[569,1402,1404,1417],{"className":1403},[572],[569,1405,1407],{"className":1406},[576],[578,1408,1409],{"xmlns":580},[582,1410,1411,1415],{},[585,1412,1413],{},[748,1414,750],{},[592,1416,750],{"encoding":594},[569,1418,1420],{"className":1419,"ariaHidden":599},[598],[569,1421,1423,1426],{"className":1422},[603],[569,1424],{"className":1425,"style":1396},[607],[569,1427,750],{"className":1428},[612]," ist die Streuung klein, am größten ist sie bei ",[569,1431,1433,1452],{"className":1432},[572],[569,1434,1436],{"className":1435},[576],[578,1437,1438],{"xmlns":580},[582,1439,1440,1449],{},[585,1441,1442,1444,1446],{},[588,1443,565],{},[698,1445,700],{},[748,1447,1448],{},"0,5",[592,1450,1451],{"encoding":594},"p = 0{,}5",[569,1453,1455,1473],{"className":1454,"ariaHidden":599},[598],[569,1456,1458,1461,1464,1467,1470],{"className":1457},[603],[569,1459],{"className":1460,"style":672},[607],[569,1462,565],{"className":1463},[612,613],[569,1465],{"className":1466,"style":796},[723],[569,1468,700],{"className":1469},[800],[569,1471],{"className":1472,"style":796},[723],[569,1474,1476,1480,1483,1491],{"className":1475},[603],[569,1477],{"className":1478,"style":1479},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,1481,1384],{"className":1482},[612],[569,1484,1486],{"className":1485},[612],[569,1487,1490],{"className":1488},[1489],"mpunct",",",[569,1492,1494],{"className":1493},[612],"5",".",[565,1497,1498,1499,1503,1504,1558,1559,1587,1588,1697,1698,1726,1727,1755],{},"Für Abschätzungen nutzt man die ",[1500,1501,1502],"strong",{},"Sigma-Regeln",": Ist ",[569,1505,1507,1527],{"className":1506},[572],[569,1508,1510],{"className":1509},[576],[578,1511,1512],{"xmlns":580},[582,1513,1514,1524],{},[585,1515,1516,1518,1521],{},[588,1517,762],{},[698,1519,1520],{},">",[748,1522,1523],{},"3",[592,1525,1526],{"encoding":594},"\\sigma > 3",[569,1528,1530,1549],{"className":1529,"ariaHidden":599},[598],[569,1531,1533,1537,1540,1543,1546],{"className":1532},[603],[569,1534],{"className":1535,"style":1536},[607],"height:0.5782em;vertical-align:-0.0391em;",[569,1538,762],{"className":1539,"style":966},[612,613],[569,1541],{"className":1542,"style":796},[723],[569,1544,1520],{"className":1545},[800],[569,1547],{"className":1548,"style":796},[723],[569,1550,1552,1555],{"className":1551},[603],[569,1553],{"className":1554,"style":1396},[607],[569,1556,1523],{"className":1557},[612]," (Laplace-Bedingung), liegt ",[569,1560,1562,1575],{"className":1561},[572],[569,1563,1565],{"className":1564},[576],[578,1566,1567],{"xmlns":580},[582,1568,1569,1573],{},[585,1570,1571],{},[588,1572,590],{},[592,1574,590],{"encoding":594},[569,1576,1578],{"className":1577,"ariaHidden":599},[598],[569,1579,1581,1584],{"className":1580},[603],[569,1582],{"className":1583,"style":608},[607],[569,1585,590],{"className":1586,"style":614},[612,613]," mit grob 68 % Wahrscheinlichkeit im Intervall ",[569,1589,1591,1629],{"className":1590},[572],[569,1592,1594],{"className":1593},[576],[578,1595,1596],{"xmlns":580},[582,1597,1598,1626],{},[585,1599,1600,1603,1605,1607,1609,1612,1616,1618,1621,1623],{},[698,1601,1602],{"stretchy":706},"[",[588,1604,696],{},[698,1606,753],{},[588,1608,762],{},[698,1610,1611],{"separator":599},";",[1613,1614,1615],"mtext",{}," ",[588,1617,696],{},[698,1619,1620],{},"+",[588,1622,762],{},[698,1624,1625],{"stretchy":706},"]",[592,1627,1628],{"encoding":594},"[\\mu - \\sigma;\\ \\mu + \\sigma]",[569,1630,1632,1653,1685],{"className":1631,"ariaHidden":599},[598],[569,1633,1635,1638,1641,1644,1647,1650],{"className":1634},[603],[569,1636],{"className":1637,"style":810},[607],[569,1639,1602],{"className":1640},[818],[569,1642,696],{"className":1643},[612,613],[569,1645],{"className":1646,"style":848},[723],[569,1648,753],{"className":1649},[852],[569,1651],{"className":1652,"style":848},[723],[569,1654,1656,1660,1663,1666,1669,1673,1676,1679,1682],{"className":1655},[603],[569,1657],{"className":1658,"style":1659},[607],"height:0.7778em;vertical-align:-0.1944em;",[569,1661,762],{"className":1662,"style":966},[612,613],[569,1664,1611],{"className":1665},[1489],[569,1667,1615],{"className":1668},[723],[569,1670],{"className":1671,"style":1672},[723],"margin-right:0.1667em;",[569,1674,696],{"className":1675},[612,613],[569,1677],{"className":1678,"style":848},[723],[569,1680,1620],{"className":1681},[852],[569,1683],{"className":1684,"style":848},[723],[569,1686,1688,1691,1694],{"className":1687},[603],[569,1689],{"className":1690,"style":810},[607],[569,1692,762],{"className":1693,"style":966},[612,613],[569,1695,1625],{"className":1696},[825],". Das ist nur eine Faustregel; der exakte Wert hängt von ",[569,1699,1701,1714],{"className":1700},[572],[569,1702,1704],{"className":1703},[576],[578,1705,1706],{"xmlns":580},[582,1707,1708,1712],{},[585,1709,1710],{},[588,1711,630],{},[592,1713,630],{"encoding":594},[569,1715,1717],{"className":1716,"ariaHidden":599},[598],[569,1718,1720,1723],{"className":1719},[603],[569,1721],{"className":1722,"style":642},[607],[569,1724,630],{"className":1725},[612,613]," und ",[569,1728,1730,1743],{"className":1729},[572],[569,1731,1733],{"className":1732},[576],[578,1734,1735],{"xmlns":580},[582,1736,1737,1741],{},[585,1738,1739],{},[588,1740,565],{},[592,1742,565],{"encoding":594},[569,1744,1746],{"className":1745,"ariaHidden":599},[598],[569,1747,1749,1752],{"className":1748},[603],[569,1750],{"className":1751,"style":672},[607],[569,1753,565],{"className":1754},[612,613]," ab.",[560,1757,1759],{"id":1758},"beispiele","Beispiele",[565,1761,1762,1763,1792,1793,1821,1822,1873,1874,2010],{},"Ein Würfel wird ",[569,1764,1766,1780],{"className":1765},[572],[569,1767,1769],{"className":1768},[576],[578,1770,1771],{"xmlns":580},[582,1772,1773,1778],{},[585,1774,1775],{},[748,1776,1777],{},"100",[592,1779,1777],{"encoding":594},[569,1781,1783],{"className":1782,"ariaHidden":599},[598],[569,1784,1786,1789],{"className":1785},[603],[569,1787],{"className":1788,"style":1396},[607],[569,1790,1777],{"className":1791},[612],"-mal geworfen, ",[569,1794,1796,1809],{"className":1795},[572],[569,1797,1799],{"className":1798},[576],[578,1800,1801],{"xmlns":580},[582,1802,1803,1807],{},[585,1804,1805],{},[588,1806,590],{},[592,1808,590],{"encoding":594},[569,1810,1812],{"className":1811,"ariaHidden":599},[598],[569,1813,1815,1818],{"className":1814},[603],[569,1816],{"className":1817,"style":608},[607],[569,1819,590],{"className":1820,"style":614},[612,613]," ist die Anzahl der Sechsen (",[569,1823,1825,1843],{"className":1824},[572],[569,1826,1828],{"className":1827},[576],[578,1829,1830],{"xmlns":580},[582,1831,1832,1840],{},[585,1833,1834,1836,1838],{},[588,1835,630],{},[698,1837,700],{},[748,1839,1777],{},[592,1841,1842],{"encoding":594},"n = 100",[569,1844,1846,1864],{"className":1845,"ariaHidden":599},[598],[569,1847,1849,1852,1855,1858,1861],{"className":1848},[603],[569,1850],{"className":1851,"style":642},[607],[569,1853,630],{"className":1854},[612,613],[569,1856],{"className":1857,"style":796},[723],[569,1859,700],{"className":1860},[800],[569,1862],{"className":1863,"style":796},[723],[569,1865,1867,1870],{"className":1866},[603],[569,1868],{"className":1869,"style":1396},[607],[569,1871,1777],{"className":1872},[612],", ",[569,1875,1877,1901],{"className":1876},[572],[569,1878,1880],{"className":1879},[576],[578,1881,1882],{"xmlns":580},[582,1883,1884,1898],{},[585,1885,1886,1888,1890],{},[588,1887,565],{},[698,1889,700],{},[1891,1892,1893,1895],"mfrac",{},[748,1894,750],{},[748,1896,1897],{},"6",[592,1899,1900],{"encoding":594},"p = \\frac{1}{6}",[569,1902,1904,1922],{"className":1903,"ariaHidden":599},[598],[569,1905,1907,1910,1913,1916,1919],{"className":1906},[603],[569,1908],{"className":1909,"style":672},[607],[569,1911,565],{"className":1912},[612,613],[569,1914],{"className":1915,"style":796},[723],[569,1917,700],{"className":1918},[800],[569,1920],{"className":1921,"style":796},[723],[569,1923,1925,1929],{"className":1924},[603],[569,1926],{"className":1927,"style":1928},[607],"height:1.1901em;vertical-align:-0.345em;",[569,1930,1932,1936,2007],{"className":1931},[612],[569,1933],{"className":1934},[818,1935],"nulldelimiter",[569,1937,1939],{"className":1938},[1891],[569,1940,1942,1998],{"className":1941},[990,991],[569,1943,1945,1995],{"className":1944},[995],[569,1946,1949,1969,1980],{"className":1947,"style":1948},[999],"height:0.8451em;",[569,1950,1952,1956],{"style":1951},"top:-2.655em;",[569,1953],{"className":1954,"style":1955},[1009],"height:3em;",[569,1957,1963],{"className":1958},[1959,1960,1961,1962],"sizing","reset-size6","size3","mtight",[569,1964,1966],{"className":1965},[612,1962],[569,1967,1897],{"className":1968},[612,1962],[569,1970,1972,1975],{"style":1971},"top:-3.23em;",[569,1973],{"className":1974,"style":1955},[1009],[569,1976],{"className":1977,"style":1979},[1978],"frac-line","border-bottom-width:0.04em;",[569,1981,1983,1986],{"style":1982},"top:-3.394em;",[569,1984],{"className":1985,"style":1955},[1009],[569,1987,1989],{"className":1988},[1959,1960,1961,1962],[569,1990,1992],{"className":1991},[612,1962],[569,1993,750],{"className":1994},[612,1962],[569,1996,1054],{"className":1997},[1053],[569,1999,2001],{"className":2000},[995],[569,2002,2005],{"className":2003,"style":2004},[999],"height:0.345em;",[569,2006],{},[569,2008],{"className":2009},[825,1935],"):",[569,2012,2014],{"className":2013},[680],[569,2015,2017,2089],{"className":2016},[572],[569,2018,2020],{"className":2019},[576],[578,2021,2022],{"xmlns":580,"display":689},[582,2023,2024,2086],{},[585,2025,2026,2028,2030,2032,2034,2040,2043,2046,2048,2050,2052,2074,2076,2081,2083],{},[588,2027,696],{},[698,2029,700],{},[748,2031,1777],{},[698,2033,719],{},[1891,2035,2036,2038],{},[748,2037,750],{},[748,2039,1897],{},[698,2041,2042],{},"≈",[748,2044,2045],{},"16,67",[723,2047],{"width":725},[588,2049,762],{},[698,2051,700],{},[766,2053,2054],{},[585,2055,2056,2058,2060,2066,2068],{},[748,2057,1777],{},[698,2059,719],{},[1891,2061,2062,2064],{},[748,2063,750],{},[748,2065,1897],{},[698,2067,719],{},[1891,2069,2070,2072],{},[748,2071,1494],{},[748,2073,1897],{},[698,2075,2042],{},[766,2077,2078],{},[748,2079,2080],{},"13,89",[698,2082,2042],{},[748,2084,2085],{},"3,73",[592,2087,2088],{"encoding":594},"\\mu = 100 \\cdot \\frac{1}{6} \\approx 16{,}67\n\\qquad\n\\sigma = \\sqrt{100 \\cdot \\frac{1}{6} \\cdot \\frac{5}{6}} \\approx \\sqrt{13{,}89} \\approx 3{,}73",[569,2090,2092,2110,2128,2210,2245,2459,2536],{"className":2091,"ariaHidden":599},[598],[569,2093,2095,2098,2101,2104,2107],{"className":2094},[603],[569,2096],{"className":2097,"style":672},[607],[569,2099,696],{"className":2100},[612,613],[569,2102],{"className":2103,"style":796},[723],[569,2105,700],{"className":2106},[800],[569,2108],{"className":2109,"style":796},[723],[569,2111,2113,2116,2119,2122,2125],{"className":2112},[603],[569,2114],{"className":2115,"style":1396},[607],[569,2117,1777],{"className":2118},[612],[569,2120],{"className":2121,"style":848},[723],[569,2123,719],{"className":2124},[852],[569,2126],{"className":2127,"style":848},[723],[569,2129,2131,2135,2201,2204,2207],{"className":2130},[603],[569,2132],{"className":2133,"style":2134},[607],"height:2.0074em;vertical-align:-0.686em;",[569,2136,2138,2141,2198],{"className":2137},[612],[569,2139],{"className":2140},[818,1935],[569,2142,2144],{"className":2143},[1891],[569,2145,2147,2189],{"className":2146},[990,991],[569,2148,2150,2186],{"className":2149},[995],[569,2151,2154,2166,2174],{"className":2152,"style":2153},[999],"height:1.3214em;",[569,2155,2157,2160],{"style":2156},"top:-2.314em;",[569,2158],{"className":2159,"style":1955},[1009],[569,2161,2163],{"className":2162},[612],[569,2164,1897],{"className":2165},[612],[569,2167,2168,2171],{"style":1971},[569,2169],{"className":2170,"style":1955},[1009],[569,2172],{"className":2173,"style":1979},[1978],[569,2175,2177,2180],{"style":2176},"top:-3.677em;",[569,2178],{"className":2179,"style":1955},[1009],[569,2181,2183],{"className":2182},[612],[569,2184,750],{"className":2185},[612],[569,2187,1054],{"className":2188},[1053],[569,2190,2192],{"className":2191},[995],[569,2193,2196],{"className":2194,"style":2195},[999],"height:0.686em;",[569,2197],{},[569,2199],{"className":2200},[825,1935],[569,2202],{"className":2203,"style":796},[723],[569,2205,2042],{"className":2206},[800],[569,2208],{"className":2209,"style":796},[723],[569,2211,2213,2216,2220,2226,2230,2233,2236,2239,2242],{"className":2212},[603],[569,2214],{"className":2215,"style":1479},[607],[569,2217,2219],{"className":2218},[612],"16",[569,2221,2223],{"className":2222},[612],[569,2224,1490],{"className":2225},[1489],[569,2227,2229],{"className":2228},[612],"67",[569,2231],{"className":2232,"style":868},[723],[569,2234,762],{"className":2235,"style":966},[612,613],[569,2237],{"className":2238,"style":796},[723],[569,2240,700],{"className":2241},[800],[569,2243],{"className":2244,"style":796},[723],[569,2246,2248,2252,2450,2453,2456],{"className":2247},[603],[569,2249],{"className":2250,"style":2251},[607],"height:2.44em;vertical-align:-0.7884em;",[569,2253,2255],{"className":2254},[612,986],[569,2256,2258,2441],{"className":2257},[990,991],[569,2259,2261,2438],{"className":2260},[995],[569,2262,2265,2421],{"className":2263,"style":2264},[999],"height:1.6516em;",[569,2266,2269,2273],{"className":2267,"style":2268},[1004],"top:-4.4em;",[569,2270],{"className":2271,"style":2272},[1009],"height:4.4em;",[569,2274,2276,2279,2282,2285,2288,2350,2353,2356,2359],{"className":2275,"style":1014},[612],[569,2277,1777],{"className":2278},[612],[569,2280],{"className":2281,"style":848},[723],[569,2283,719],{"className":2284},[852],[569,2286],{"className":2287,"style":848},[723],[569,2289,2291,2294,2347],{"className":2290},[612],[569,2292],{"className":2293},[818,1935],[569,2295,2297],{"className":2296},[1891],[569,2298,2300,2339],{"className":2299},[990,991],[569,2301,2303,2336],{"className":2302},[995],[569,2304,2306,2317,2325],{"className":2305,"style":2153},[999],[569,2307,2308,2311],{"style":2156},[569,2309],{"className":2310,"style":1955},[1009],[569,2312,2314],{"className":2313},[612],[569,2315,1897],{"className":2316},[612],[569,2318,2319,2322],{"style":1971},[569,2320],{"className":2321,"style":1955},[1009],[569,2323],{"className":2324,"style":1979},[1978],[569,2326,2327,2330],{"style":2176},[569,2328],{"className":2329,"style":1955},[1009],[569,2331,2333],{"className":2332},[612],[569,2334,750],{"className":2335},[612],[569,2337,1054],{"className":2338},[1053],[569,2340,2342],{"className":2341},[995],[569,2343,2345],{"className":2344,"style":2195},[999],[569,2346],{},[569,2348],{"className":2349},[825,1935],[569,2351],{"className":2352,"style":848},[723],[569,2354,719],{"className":2355},[852],[569,2357],{"className":2358,"style":848},[723],[569,2360,2362,2365,2418],{"className":2361},[612],[569,2363],{"className":2364},[818,1935],[569,2366,2368],{"className":2367},[1891],[569,2369,2371,2410],{"className":2370},[990,991],[569,2372,2374,2407],{"className":2373},[995],[569,2375,2377,2388,2396],{"className":2376,"style":2153},[999],[569,2378,2379,2382],{"style":2156},[569,2380],{"className":2381,"style":1955},[1009],[569,2383,2385],{"className":2384},[612],[569,2386,1897],{"className":2387},[612],[569,2389,2390,2393],{"style":1971},[569,2391],{"className":2392,"style":1955},[1009],[569,2394],{"className":2395,"style":1979},[1978],[569,2397,2398,2401],{"style":2176},[569,2399],{"className":2400,"style":1955},[1009],[569,2402,2404],{"className":2403},[612],[569,2405,1494],{"className":2406},[612],[569,2408,1054],{"className":2409},[1053],[569,2411,2413],{"className":2412},[995],[569,2414,2416],{"className":2415,"style":2195},[999],[569,2417],{},[569,2419],{"className":2420},[825,1935],[569,2422,2424,2427],{"style":2423},"top:-3.6116em;",[569,2425],{"className":2426,"style":2272},[1009],[569,2428,2431],{"className":2429,"style":2430},[1036],"min-width:1.02em;height:2.48em;",[1039,2432,2435],{"xmlns":1041,"width":1042,"height":2433,"viewBox":2434,"preserveAspectRatio":1045},"2.48em","0 0 400000 2592",[1047,2436],{"d":2437},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[569,2439,1054],{"className":2440},[1053],[569,2442,2444],{"className":2443},[995],[569,2445,2448],{"className":2446,"style":2447},[999],"height:0.7884em;",[569,2449],{},[569,2451],{"className":2452,"style":796},[723],[569,2454,2042],{"className":2455},[800],[569,2457],{"className":2458,"style":796},[723],[569,2460,2462,2466,2527,2530,2533],{"className":2461},[603],[569,2463],{"className":2464,"style":2465},[607],"height:1.24em;vertical-align:-0.2811em;",[569,2467,2469],{"className":2468},[612,986],[569,2470,2472,2518],{"className":2471},[990,991],[569,2473,2475,2515],{"className":2474},[995],[569,2476,2479,2502],{"className":2477,"style":2478},[999],"height:0.9589em;",[569,2480,2482,2485],{"className":2481,"style":1005},[1004],[569,2483],{"className":2484,"style":1010},[1009],[569,2486,2488,2492,2498],{"className":2487,"style":1014},[612],[569,2489,2491],{"className":2490},[612],"13",[569,2493,2495],{"className":2494},[612],[569,2496,1490],{"className":2497},[1489],[569,2499,2501],{"className":2500},[612],"89",[569,2503,2505,2508],{"style":2504},"top:-2.9189em;",[569,2506],{"className":2507,"style":1010},[1009],[569,2509,2511],{"className":2510,"style":1037},[1036],[1039,2512,2513],{"xmlns":1041,"width":1042,"height":1043,"viewBox":1044,"preserveAspectRatio":1045},[1047,2514],{"d":1049},[569,2516,1054],{"className":2517},[1053],[569,2519,2521],{"className":2520},[995],[569,2522,2525],{"className":2523,"style":2524},[999],"height:0.2811em;",[569,2526],{},[569,2528],{"className":2529,"style":796},[723],[569,2531,2042],{"className":2532},[800],[569,2534],{"className":2535,"style":796},[723],[569,2537,2539,2542,2545,2551],{"className":2538},[603],[569,2540],{"className":2541,"style":1479},[607],[569,2543,1523],{"className":2544},[612],[569,2546,2548],{"className":2547},[612],[569,2549,1490],{"className":2550},[1489],[569,2552,2554],{"className":2553},[612],"73",[565,2556,2557,2558,2641,2642,1726,2745,2848,2849,2877,2878,2906,2907,3032],{},"Weil ",[569,2559,2561,2583],{"className":2560},[572],[569,2562,2564],{"className":2563},[576],[578,2565,2566],{"xmlns":580},[582,2567,2568,2580],{},[585,2569,2570,2572,2574,2576,2578],{},[588,2571,762],{},[698,2573,2042],{},[748,2575,2085],{},[698,2577,1520],{},[748,2579,1523],{},[592,2581,2582],{"encoding":594},"\\sigma \\approx 3{,}73 > 3",[569,2584,2586,2605,2632],{"className":2585,"ariaHidden":599},[598],[569,2587,2589,2593,2596,2599,2602],{"className":2588},[603],[569,2590],{"className":2591,"style":2592},[607],"height:0.4831em;",[569,2594,762],{"className":2595,"style":966},[612,613],[569,2597],{"className":2598,"style":796},[723],[569,2600,2042],{"className":2601},[800],[569,2603],{"className":2604,"style":796},[723],[569,2606,2608,2611,2614,2620,2623,2626,2629],{"className":2607},[603],[569,2609],{"className":2610,"style":1479},[607],[569,2612,1523],{"className":2613},[612],[569,2615,2617],{"className":2616},[612],[569,2618,1490],{"className":2619},[1489],[569,2621,2554],{"className":2622},[612],[569,2624],{"className":2625,"style":796},[723],[569,2627,1520],{"className":2628},[800],[569,2630],{"className":2631,"style":796},[723],[569,2633,2635,2638],{"className":2634},[603],[569,2636],{"className":2637,"style":1396},[607],[569,2639,1523],{"className":2640},[612]," ist, gilt die Sigma-Regel: Die Anzahl der Sechsen liegt mit grob 68 % Wahrscheinlichkeit zwischen ",[569,2643,2645,2668],{"className":2644},[572],[569,2646,2648],{"className":2647},[576],[578,2649,2650],{"xmlns":580},[582,2651,2652,2665],{},[585,2653,2654,2656,2658,2660,2662],{},[748,2655,2045],{},[698,2657,753],{},[748,2659,2085],{},[698,2661,2042],{},[748,2663,2664],{},"12,94",[592,2666,2667],{"encoding":594},"16{,}67 - 3{,}73 \\approx 12{,}94",[569,2669,2671,2698,2725],{"className":2670,"ariaHidden":599},[598],[569,2672,2674,2677,2680,2686,2689,2692,2695],{"className":2673},[603],[569,2675],{"className":2676,"style":1479},[607],[569,2678,2219],{"className":2679},[612],[569,2681,2683],{"className":2682},[612],[569,2684,1490],{"className":2685},[1489],[569,2687,2229],{"className":2688},[612],[569,2690],{"className":2691,"style":848},[723],[569,2693,753],{"className":2694},[852],[569,2696],{"className":2697,"style":848},[723],[569,2699,2701,2704,2707,2713,2716,2719,2722],{"className":2700},[603],[569,2702],{"className":2703,"style":1479},[607],[569,2705,1523],{"className":2706},[612],[569,2708,2710],{"className":2709},[612],[569,2711,1490],{"className":2712},[1489],[569,2714,2554],{"className":2715},[612],[569,2717],{"className":2718,"style":796},[723],[569,2720,2042],{"className":2721},[800],[569,2723],{"className":2724,"style":796},[723],[569,2726,2728,2731,2735,2741],{"className":2727},[603],[569,2729],{"className":2730,"style":1479},[607],[569,2732,2734],{"className":2733},[612],"12",[569,2736,2738],{"className":2737},[612],[569,2739,1490],{"className":2740},[1489],[569,2742,2744],{"className":2743},[612],"94",[569,2746,2748,2771],{"className":2747},[572],[569,2749,2751],{"className":2750},[576],[578,2752,2753],{"xmlns":580},[582,2754,2755,2768],{},[585,2756,2757,2759,2761,2763,2765],{},[748,2758,2045],{},[698,2760,1620],{},[748,2762,2085],{},[698,2764,2042],{},[748,2766,2767],{},"20,39",[592,2769,2770],{"encoding":594},"16{,}67 + 3{,}73 \\approx 20{,}39",[569,2772,2774,2801,2828],{"className":2773,"ariaHidden":599},[598],[569,2775,2777,2780,2783,2789,2792,2795,2798],{"className":2776},[603],[569,2778],{"className":2779,"style":1479},[607],[569,2781,2219],{"className":2782},[612],[569,2784,2786],{"className":2785},[612],[569,2787,1490],{"className":2788},[1489],[569,2790,2229],{"className":2791},[612],[569,2793],{"className":2794,"style":848},[723],[569,2796,1620],{"className":2797},[852],[569,2799],{"className":2800,"style":848},[723],[569,2802,2804,2807,2810,2816,2819,2822,2825],{"className":2803},[603],[569,2805],{"className":2806,"style":1479},[607],[569,2808,1523],{"className":2809},[612],[569,2811,2813],{"className":2812},[612],[569,2814,1490],{"className":2815},[1489],[569,2817,2554],{"className":2818},[612],[569,2820],{"className":2821,"style":796},[723],[569,2823,2042],{"className":2824},[800],[569,2826],{"className":2827,"style":796},[723],[569,2829,2831,2834,2838,2844],{"className":2830},[603],[569,2832],{"className":2833,"style":1479},[607],[569,2835,2837],{"className":2836},[612],"20",[569,2839,2841],{"className":2840},[612],[569,2842,1490],{"className":2843},[1489],[569,2845,2847],{"className":2846},[612],"39",", also bei ",[569,2850,2852,2865],{"className":2851},[572],[569,2853,2855],{"className":2854},[576],[578,2856,2857],{"xmlns":580},[582,2858,2859,2863],{},[585,2860,2861],{},[748,2862,2491],{},[592,2864,2491],{"encoding":594},[569,2866,2868],{"className":2867,"ariaHidden":599},[598],[569,2869,2871,2874],{"className":2870},[603],[569,2872],{"className":2873,"style":1396},[607],[569,2875,2491],{"className":2876},[612]," bis ",[569,2879,2881,2894],{"className":2880},[572],[569,2882,2884],{"className":2883},[576],[578,2885,2886],{"xmlns":580},[582,2887,2888,2892],{},[585,2889,2890],{},[748,2891,2837],{},[592,2893,2837],{"encoding":594},[569,2895,2897],{"className":2896,"ariaHidden":599},[598],[569,2898,2900,2903],{"className":2899},[603],[569,2901],{"className":2902,"style":1396},[607],[569,2904,2837],{"className":2905},[612]," Sechsen. Exakt mit der Binomialverteilung berechnet ist ",[569,2908,2910,2945],{"className":2909},[572],[569,2911,2913],{"className":2912},[576],[578,2914,2915],{"xmlns":580},[582,2916,2917,2942],{},[585,2918,2919,2922,2924,2926,2929,2931,2933,2935,2937,2939],{},[588,2920,2921],{},"P",[698,2923,707],{"stretchy":706},[748,2925,2491],{},[698,2927,2928],{},"≤",[588,2930,590],{},[698,2932,2928],{},[748,2934,2837],{},[698,2936,712],{"stretchy":706},[698,2938,2042],{},[748,2940,2941],{},"0,718",[592,2943,2944],{"encoding":594},"P(13 \\leq X \\leq 20) \\approx 0{,}718",[569,2946,2948,2973,2992,3013],{"className":2947,"ariaHidden":599},[598],[569,2949,2951,2954,2958,2961,2964,2967,2970],{"className":2950},[603],[569,2952],{"className":2953,"style":810},[607],[569,2955,2921],{"className":2956,"style":2957},[612,613],"margin-right:0.1389em;",[569,2959,707],{"className":2960},[818],[569,2962,2491],{"className":2963},[612],[569,2965],{"className":2966,"style":796},[723],[569,2968,2928],{"className":2969},[800],[569,2971],{"className":2972,"style":796},[723],[569,2974,2976,2980,2983,2986,2989],{"className":2975},[603],[569,2977],{"className":2978,"style":2979},[607],"height:0.8193em;vertical-align:-0.136em;",[569,2981,590],{"className":2982,"style":614},[612,613],[569,2984],{"className":2985,"style":796},[723],[569,2987,2928],{"className":2988},[800],[569,2990],{"className":2991,"style":796},[723],[569,2993,2995,2998,3001,3004,3007,3010],{"className":2994},[603],[569,2996],{"className":2997,"style":810},[607],[569,2999,2837],{"className":3000},[612],[569,3002,712],{"className":3003},[825],[569,3005],{"className":3006,"style":796},[723],[569,3008,2042],{"className":3009},[800],[569,3011],{"className":3012,"style":796},[723],[569,3014,3016,3019,3022,3028],{"className":3015},[603],[569,3017],{"className":3018,"style":1479},[607],[569,3020,1384],{"className":3021},[612],[569,3023,3025],{"className":3024},[612],[569,3026,1490],{"className":3027},[1489],[569,3029,3031],{"className":3030},[612],"718",", also etwa 72 %.",[565,3034,3035,3036,3065,3066,3106],{},"Eine Fluggesellschaft hat ",[569,3037,3039,3053],{"className":3038},[572],[569,3040,3042],{"className":3041},[576],[578,3043,3044],{"xmlns":580},[582,3045,3046,3051],{},[585,3047,3048],{},[748,3049,3050],{},"200",[592,3052,3050],{"encoding":594},[569,3054,3056],{"className":3055,"ariaHidden":599},[598],[569,3057,3059,3062],{"className":3058},[603],[569,3060],{"className":3061,"style":1396},[607],[569,3063,3050],{"className":3064},[612]," Buchungen, jeder Fluggast erscheint mit Wahrscheinlichkeit ",[569,3067,3069,3084],{"className":3068},[572],[569,3070,3072],{"className":3071},[576],[578,3073,3074],{"xmlns":580},[582,3075,3076,3081],{},[585,3077,3078],{},[748,3079,3080],{},"0,08",[592,3082,3083],{"encoding":594},"0{,}08",[569,3085,3087],{"className":3086,"ariaHidden":599},[598],[569,3088,3090,3093,3096,3102],{"className":3089},[603],[569,3091],{"className":3092,"style":1479},[607],[569,3094,1384],{"className":3095},[612],[569,3097,3099],{"className":3098},[612],[569,3100,1490],{"className":3101},[1489],[569,3103,3105],{"className":3104},[612],"08"," nicht. Für die Anzahl der Nichterscheinenden gilt (unter der Annahme, dass die Fluggäste unabhängig voneinander handeln):",[569,3108,3110],{"className":3109},[680],[569,3111,3113,3172],{"className":3112},[572],[569,3114,3116],{"className":3115},[576],[578,3117,3118],{"xmlns":580,"display":689},[582,3119,3120,3169],{},[585,3121,3122,3124,3126,3128,3130,3132,3134,3136,3138,3140,3142,3157,3159,3164,3166],{},[588,3123,696],{},[698,3125,700],{},[748,3127,3050],{},[698,3129,719],{},[748,3131,3080],{},[698,3133,700],{},[748,3135,2219],{},[723,3137],{"width":725},[588,3139,762],{},[698,3141,700],{},[766,3143,3144],{},[585,3145,3146,3148,3150,3152,3154],{},[748,3147,3050],{},[698,3149,719],{},[748,3151,3080],{},[698,3153,719],{},[748,3155,3156],{},"0,92",[698,3158,700],{},[766,3160,3161],{},[748,3162,3163],{},"14,72",[698,3165,2042],{},[748,3167,3168],{},"3,84",[592,3170,3171],{"encoding":594},"\\mu = 200 \\cdot 0{,}08 = 16\n\\qquad\n\\sigma = \\sqrt{200 \\cdot 0{,}08 \\cdot 0{,}92} = \\sqrt{14{,}72} \\approx 3{,}84",[569,3173,3175,3193,3211,3238,3262,3367,3440],{"className":3174,"ariaHidden":599},[598],[569,3176,3178,3181,3184,3187,3190],{"className":3177},[603],[569,3179],{"className":3180,"style":672},[607],[569,3182,696],{"className":3183},[612,613],[569,3185],{"className":3186,"style":796},[723],[569,3188,700],{"className":3189},[800],[569,3191],{"className":3192,"style":796},[723],[569,3194,3196,3199,3202,3205,3208],{"className":3195},[603],[569,3197],{"className":3198,"style":1396},[607],[569,3200,3050],{"className":3201},[612],[569,3203],{"className":3204,"style":848},[723],[569,3206,719],{"className":3207},[852],[569,3209],{"className":3210,"style":848},[723],[569,3212,3214,3217,3220,3226,3229,3232,3235],{"className":3213},[603],[569,3215],{"className":3216,"style":1479},[607],[569,3218,1384],{"className":3219},[612],[569,3221,3223],{"className":3222},[612],[569,3224,1490],{"className":3225},[1489],[569,3227,3105],{"className":3228},[612],[569,3230],{"className":3231,"style":796},[723],[569,3233,700],{"className":3234},[800],[569,3236],{"className":3237,"style":796},[723],[569,3239,3241,3244,3247,3250,3253,3256,3259],{"className":3240},[603],[569,3242],{"className":3243,"style":1396},[607],[569,3245,2219],{"className":3246},[612],[569,3248],{"className":3249,"style":868},[723],[569,3251,762],{"className":3252,"style":966},[612,613],[569,3254],{"className":3255,"style":796},[723],[569,3257,700],{"className":3258},[800],[569,3260],{"className":3261,"style":796},[723],[569,3263,3265,3268,3358,3361,3364],{"className":3264},[603],[569,3266],{"className":3267,"style":2465},[607],[569,3269,3271],{"className":3270},[612,986],[569,3272,3274,3350],{"className":3273},[990,991],[569,3275,3277,3347],{"className":3276},[995],[569,3278,3280,3335],{"className":3279,"style":2478},[999],[569,3281,3283,3286],{"className":3282,"style":1005},[1004],[569,3284],{"className":3285,"style":1010},[1009],[569,3287,3289,3292,3295,3298,3301,3304,3310,3313,3316,3319,3322,3325,3331],{"className":3288,"style":1014},[612],[569,3290,3050],{"className":3291},[612],[569,3293],{"className":3294,"style":848},[723],[569,3296,719],{"className":3297},[852],[569,3299],{"className":3300,"style":848},[723],[569,3302,1384],{"className":3303},[612],[569,3305,3307],{"className":3306},[612],[569,3308,1490],{"className":3309},[1489],[569,3311,3105],{"className":3312},[612],[569,3314],{"className":3315,"style":848},[723],[569,3317,719],{"className":3318},[852],[569,3320],{"className":3321,"style":848},[723],[569,3323,1384],{"className":3324},[612],[569,3326,3328],{"className":3327},[612],[569,3329,1490],{"className":3330},[1489],[569,3332,3334],{"className":3333},[612],"92",[569,3336,3337,3340],{"style":2504},[569,3338],{"className":3339,"style":1010},[1009],[569,3341,3343],{"className":3342,"style":1037},[1036],[1039,3344,3345],{"xmlns":1041,"width":1042,"height":1043,"viewBox":1044,"preserveAspectRatio":1045},[1047,3346],{"d":1049},[569,3348,1054],{"className":3349},[1053],[569,3351,3353],{"className":3352},[995],[569,3354,3356],{"className":3355,"style":2524},[999],[569,3357],{},[569,3359],{"className":3360,"style":796},[723],[569,3362,700],{"className":3363},[800],[569,3365],{"className":3366,"style":796},[723],[569,3368,3370,3373,3431,3434,3437],{"className":3369},[603],[569,3371],{"className":3372,"style":2465},[607],[569,3374,3376],{"className":3375},[612,986],[569,3377,3379,3423],{"className":3378},[990,991],[569,3380,3382,3420],{"className":3381},[995],[569,3383,3385,3408],{"className":3384,"style":2478},[999],[569,3386,3388,3391],{"className":3387,"style":1005},[1004],[569,3389],{"className":3390,"style":1010},[1009],[569,3392,3394,3398,3404],{"className":3393,"style":1014},[612],[569,3395,3397],{"className":3396},[612],"14",[569,3399,3401],{"className":3400},[612],[569,3402,1490],{"className":3403},[1489],[569,3405,3407],{"className":3406},[612],"72",[569,3409,3410,3413],{"style":2504},[569,3411],{"className":3412,"style":1010},[1009],[569,3414,3416],{"className":3415,"style":1037},[1036],[1039,3417,3418],{"xmlns":1041,"width":1042,"height":1043,"viewBox":1044,"preserveAspectRatio":1045},[1047,3419],{"d":1049},[569,3421,1054],{"className":3422},[1053],[569,3424,3426],{"className":3425},[995],[569,3427,3429],{"className":3428,"style":2524},[999],[569,3430],{},[569,3432],{"className":3433,"style":796},[723],[569,3435,2042],{"className":3436},[800],[569,3438],{"className":3439,"style":796},[723],[569,3441,3443,3446,3449,3455],{"className":3442},[603],[569,3444],{"className":3445,"style":1479},[607],[569,3447,1523],{"className":3448},[612],[569,3450,3452],{"className":3451},[612],[569,3453,1490],{"className":3454},[1489],[569,3456,3458],{"className":3457},[612],"84",[560,3460,3462],{"id":3461},"typische-fehler","Typische Fehler",[3464,3465,3466,3654,3820,3823],"ul",{},[3467,3468,3469,3470,3575,3576,3614,3615,3653],"li",{},"Die Wurzel vergessen: ",[569,3471,3473,3503],{"className":3472},[572],[569,3474,3476],{"className":3475},[576],[578,3477,3478],{"xmlns":580},[582,3479,3480,3500],{},[585,3481,3482,3484,3486,3488,3490,3492,3494,3496,3498],{},[588,3483,630],{},[698,3485,719],{},[588,3487,565],{},[698,3489,719],{},[698,3491,707],{"stretchy":706},[748,3493,750],{},[698,3495,753],{},[588,3497,565],{},[698,3499,712],{"stretchy":706},[592,3501,3502],{"encoding":594},"n \\cdot p \\cdot (1-p)",[569,3504,3506,3524,3542,3563],{"className":3505,"ariaHidden":599},[598],[569,3507,3509,3512,3515,3518,3521],{"className":3508},[603],[569,3510],{"className":3511,"style":841},[607],[569,3513,630],{"className":3514},[612,613],[569,3516],{"className":3517,"style":848},[723],[569,3519,719],{"className":3520},[852],[569,3522],{"className":3523,"style":848},[723],[569,3525,3527,3530,3533,3536,3539],{"className":3526},[603],[569,3528],{"className":3529,"style":914},[607],[569,3531,565],{"className":3532},[612,613],[569,3534],{"className":3535,"style":848},[723],[569,3537,719],{"className":3538},[852],[569,3540],{"className":3541,"style":848},[723],[569,3543,3545,3548,3551,3554,3557,3560],{"className":3544},[603],[569,3546],{"className":3547,"style":810},[607],[569,3549,707],{"className":3550},[818],[569,3552,750],{"className":3553},[612],[569,3555],{"className":3556,"style":848},[723],[569,3558,753],{"className":3559},[852],[569,3561],{"className":3562,"style":848},[723],[569,3564,3566,3569,3572],{"className":3565},[603],[569,3567],{"className":3568,"style":810},[607],[569,3570,565],{"className":3571},[612,613],[569,3573,712],{"className":3574},[825]," ist die Varianz, nicht die Standardabweichung. Im Würfelbeispiel wäre ",[569,3577,3579,3593],{"className":3578},[572],[569,3580,3582],{"className":3581},[576],[578,3583,3584],{"xmlns":580},[582,3585,3586,3590],{},[585,3587,3588],{},[748,3589,2080],{},[592,3591,3592],{"encoding":594},"13{,}89",[569,3594,3596],{"className":3595,"ariaHidden":599},[598],[569,3597,3599,3602,3605,3611],{"className":3598},[603],[569,3600],{"className":3601,"style":1479},[607],[569,3603,2491],{"className":3604},[612],[569,3606,3608],{"className":3607},[612],[569,3609,1490],{"className":3610},[1489],[569,3612,2501],{"className":3613},[612]," statt ",[569,3616,3618,3632],{"className":3617},[572],[569,3619,3621],{"className":3620},[576],[578,3622,3623],{"xmlns":580},[582,3624,3625,3629],{},[585,3626,3627],{},[748,3628,2085],{},[592,3630,3631],{"encoding":594},"3{,}73",[569,3633,3635],{"className":3634,"ariaHidden":599},[598],[569,3636,3638,3641,3644,3650],{"className":3637},[603],[569,3639],{"className":3640,"style":1479},[607],[569,3642,1523],{"className":3643},[612],[569,3645,3647],{"className":3646},[612],[569,3648,1490],{"className":3649},[1489],[569,3651,2554],{"className":3652},[612]," falsch.",[3467,3655,3656,1726,3684,3736,3737,3819],{},[569,3657,3659,3672],{"className":3658},[572],[569,3660,3662],{"className":3661},[576],[578,3663,3664],{"xmlns":580},[582,3665,3666,3670],{},[585,3667,3668],{},[588,3669,565],{},[592,3671,565],{"encoding":594},[569,3673,3675],{"className":3674,"ariaHidden":599},[598],[569,3676,3678,3681],{"className":3677},[603],[569,3679],{"className":3680,"style":672},[607],[569,3682,565],{"className":3683},[612,613],[569,3685,3687,3705],{"className":3686},[572],[569,3688,3690],{"className":3689},[576],[578,3691,3692],{"xmlns":580},[582,3693,3694,3702],{},[585,3695,3696,3698,3700],{},[748,3697,750],{},[698,3699,753],{},[588,3701,565],{},[592,3703,3704],{"encoding":594},"1 - p",[569,3706,3708,3727],{"className":3707,"ariaHidden":599},[598],[569,3709,3711,3715,3718,3721,3724],{"className":3710},[603],[569,3712],{"className":3713,"style":3714},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,3716,750],{"className":3717},[612],[569,3719],{"className":3720,"style":848},[723],[569,3722,753],{"className":3723},[852],[569,3725],{"className":3726,"style":848},[723],[569,3728,3730,3733],{"className":3729},[603],[569,3731],{"className":3732,"style":672},[607],[569,3734,565],{"className":3735},[612,613]," verwechseln, etwa im Flugbeispiel ",[569,3738,3740,3762],{"className":3739},[572],[569,3741,3743],{"className":3742},[576],[578,3744,3745],{"xmlns":580},[582,3746,3747,3759],{},[585,3748,3749,3751,3753,3755,3757],{},[588,3750,696],{},[698,3752,700],{},[748,3754,3050],{},[698,3756,719],{},[748,3758,3156],{},[592,3760,3761],{"encoding":594},"\\mu = 200 \\cdot 0{,}92",[569,3763,3765,3783,3801],{"className":3764,"ariaHidden":599},[598],[569,3766,3768,3771,3774,3777,3780],{"className":3767},[603],[569,3769],{"className":3770,"style":672},[607],[569,3772,696],{"className":3773},[612,613],[569,3775],{"className":3776,"style":796},[723],[569,3778,700],{"className":3779},[800],[569,3781],{"className":3782,"style":796},[723],[569,3784,3786,3789,3792,3795,3798],{"className":3785},[603],[569,3787],{"className":3788,"style":1396},[607],[569,3790,3050],{"className":3791},[612],[569,3793],{"className":3794,"style":848},[723],[569,3796,719],{"className":3797},[852],[569,3799],{"className":3800,"style":848},[723],[569,3802,3804,3807,3810,3816],{"className":3803},[603],[569,3805],{"className":3806,"style":1479},[607],[569,3808,1384],{"className":3809},[612],[569,3811,3813],{"className":3812},[612],[569,3814,1490],{"className":3815},[1489],[569,3817,3334],{"className":3818},[612]," rechnen. Das ist die erwartete Zahl der Erscheinenden, nicht der Nichterscheinenden.",[3467,3821,3822],{},"Die Formeln auf Zufallsgrößen anwenden, die nicht binomialverteilt sind, z.B. auf eine Augenzahl oder beim Ziehen ohne Zurücklegen aus einer kleinen Urne.",[3467,3824,3825,3826,3876,3877,3905],{},"Die Sigma-Regeln ohne Prüfung von ",[569,3827,3829,3846],{"className":3828},[572],[569,3830,3832],{"className":3831},[576],[578,3833,3834],{"xmlns":580},[582,3835,3836,3844],{},[585,3837,3838,3840,3842],{},[588,3839,762],{},[698,3841,1520],{},[748,3843,1523],{},[592,3845,1526],{"encoding":594},[569,3847,3849,3867],{"className":3848,"ariaHidden":599},[598],[569,3850,3852,3855,3858,3861,3864],{"className":3851},[603],[569,3853],{"className":3854,"style":1536},[607],[569,3856,762],{"className":3857,"style":966},[612,613],[569,3859],{"className":3860,"style":796},[723],[569,3862,1520],{"className":3863},[800],[569,3865],{"className":3866,"style":796},[723],[569,3868,3870,3873],{"className":3869},[603],[569,3871],{"className":3872,"style":1396},[607],[569,3874,1523],{"className":3875},[612]," verwenden. Bei kleinem ",[569,3878,3880,3893],{"className":3879},[572],[569,3881,3883],{"className":3882},[576],[578,3884,3885],{"xmlns":580},[582,3886,3887,3891],{},[585,3888,3889],{},[588,3890,762],{},[592,3892,1298],{"encoding":594},[569,3894,3896],{"className":3895,"ariaHidden":599},[598],[569,3897,3899,3902],{"className":3898},[603],[569,3900],{"className":3901,"style":642},[607],[569,3903,762],{"className":3904,"style":966},[612,613]," sind die Näherungen ungenau.",{"title":3907,"searchDepth":3908,"depth":3908,"links":3909},"",2,[3910,3911,3912],{"id":562,"depth":3908,"text":563},{"id":1758,"depth":3908,"text":1759},{"id":3461,"depth":3908,"text":3462},[3914,3917,3920,3923,3926,3929,3932,3935,3937,3939,3941,3944,3946,3949],{"lhs":3915,"rhs":3916},"0*(1-p)^3 + 1*3*p*(1-p)^2 + 2*3*p^2*(1-p) + 3*p^3","3*p",{"lhs":3918,"rhs":3919},"(0-3*p)^2*(1-p)^3 + (1-3*p)^2*3*p*(1-p)^2 + (2-3*p)^2*3*p^2*(1-p) + (3-3*p)^2*p^3","3*p*(1-p)",{"lhs":3921,"rhs":3922},"round(100 * 1\u002F6, 2)","16.67",{"lhs":3924,"rhs":3925},"round(100 * 1\u002F6 * 5\u002F6, 2)","13.89",{"lhs":3927,"rhs":3928},"round(sqrt(100 * 1\u002F6 * 5\u002F6), 2)","3.73",{"lhs":3930,"rhs":3931},"round(100\u002F6 - sqrt(100 * 1\u002F6 * 5\u002F6), 2)","12.94",{"lhs":3933,"rhs":3934},"round(100\u002F6 + sqrt(100 * 1\u002F6 * 5\u002F6), 2)","20.39",{"lhs":3936,"rhs":1523},"min(sqrt(100 * 1\u002F6 * 5\u002F6), 3)",{"lhs":3938,"rhs":2491},"ceil(100\u002F6 - sqrt(100 * 1\u002F6 * 5\u002F6))",{"lhs":3940,"rhs":2837},"floor(100\u002F6 + sqrt(100 * 1\u002F6 * 5\u002F6))",{"lhs":3942,"rhs":3943},"round(combinations(100, 13) * (1\u002F6)^13 * (5\u002F6)^87 + combinations(100, 14) * (1\u002F6)^14 * (5\u002F6)^86 + combinations(100, 15) * (1\u002F6)^15 * (5\u002F6)^85 + combinations(100, 16) * (1\u002F6)^16 * (5\u002F6)^84 + combinations(100, 17) * (1\u002F6)^17 * (5\u002F6)^83 + combinations(100, 18) * (1\u002F6)^18 * (5\u002F6)^82 + combinations(100, 19) * (1\u002F6)^19 * (5\u002F6)^81 + combinations(100, 20) * (1\u002F6)^20 * (5\u002F6)^80, 3)","0.718",{"lhs":3945,"rhs":2219},"200 * 0.08",{"lhs":3947,"rhs":3948},"200 * 0.08 * 0.92","14.72",{"lhs":3950,"rhs":3951},"round(sqrt(200 * 0.08 * 0.92), 2)","3.84","X \\text{ binomialverteilt},\\ n \\in \\mathbb{N},\\ n \\geq 1,\\ 0 \\leq p \\leq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">binomialverteilt\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 \\leq p \\leq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","binomial-mean-sd","\\mu = n \\cdot p,\\quad \\sigma = \\sqrt{n \\cdot p \\cdot (1-p)}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>σ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu = n \\cdot p,\\quad \\sigma = \\sqrt{n \\cdot p \\cdot (1-p)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.24em;vertical-align:-0.2561em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9839em;\">\u003Cspan class=\"svg-align\" style=\"top:-3.2em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:1em;\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9439em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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