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Im Histogramm gehört zum Wert ",[569,980,982,996],{"className":981},[572],[569,983,985],{"className":984},[576],[578,986,987],{"xmlns":580},[582,988,989,994],{},[585,990,991],{},[588,992,993],{},"k",[592,995,993],{"encoding":594},[569,997,999],{"className":998,"ariaHidden":599},[598],[569,1000,1002,1006],{"className":1001},[603],[569,1003],{"className":1004,"style":1005},[607],"height:0.6944em;",[569,1007,993],{"className":1008,"style":1009},[612,613],"margin-right:0.0315em;"," ein Balken von ",[569,1012,1014,1032],{"className":1013},[572],[569,1015,1017],{"className":1016},[576],[578,1018,1019],{"xmlns":580},[582,1020,1021,1029],{},[585,1022,1023,1025,1027],{},[588,1024,993],{},[636,1026,720],{},[715,1028,942],{},[592,1030,1031],{"encoding":594},"k - 0{,}5",[569,1033,1035,1054],{"className":1034,"ariaHidden":599},[598],[569,1036,1038,1042,1045,1048,1051],{"className":1037},[603],[569,1039],{"className":1040,"style":1041},[607],"height:0.7778em;vertical-align:-0.0833em;",[569,1043,993],{"className":1044,"style":1009},[612,613],[569,1046],{"className":1047,"style":806},[662],[569,1049,720],{"className":1050},[810],[569,1052],{"className":1053,"style":806},[662],[569,1055,1057,1060,1063,1069],{"className":1056},[603],[569,1058],{"className":1059,"style":955},[607],[569,1061,962],{"className":1062},[612],[569,1064,1066],{"className":1065},[612],[569,1067,970],{"className":1068},[969],[569,1070,974],{"className":1071},[612]," bis ",[569,1074,1076,1094],{"className":1075},[572],[569,1077,1079],{"className":1078},[576],[578,1080,1081],{"xmlns":580},[582,1082,1083,1091],{},[585,1084,1085,1087,1089],{},[588,1086,993],{},[636,1088,939],{},[715,1090,942],{},[592,1092,1093],{"encoding":594},"k + 0{,}5",[569,1095,1097,1115],{"className":1096,"ariaHidden":599},[598],[569,1098,1100,1103,1106,1109,1112],{"className":1099},[603],[569,1101],{"className":1102,"style":1041},[607],[569,1104,993],{"className":1105,"style":1009},[612,613],[569,1107],{"className":1108,"style":806},[662],[569,1110,939],{"className":1111},[810],[569,1113],{"className":1114,"style":806},[662],[569,1116,1118,1121,1124,1130],{"className":1117},[603],[569,1119],{"className":1120,"style":955},[607],[569,1122,962],{"className":1123},[612],[569,1125,1127],{"className":1126},[612],[569,1128,970],{"className":1129},[969],[569,1131,974],{"className":1132},[612],". Damit der Balken bei ",[569,1135,1137,1150],{"className":1136},[572],[569,1138,1140],{"className":1139},[576],[578,1141,1142],{"xmlns":580},[582,1143,1144,1148],{},[585,1145,1146],{},[588,1147,993],{},[592,1149,993],{"encoding":594},[569,1151,1153],{"className":1152,"ariaHidden":599},[598],[569,1154,1156,1159],{"className":1155},[603],[569,1157],{"className":1158,"style":1005},[607],[569,1160,993],{"className":1161,"style":1009},[612,613]," voll mitzählt, integriert man bis ",[569,1164,1166,1183],{"className":1165},[572],[569,1167,1169],{"className":1168},[576],[578,1170,1171],{"xmlns":580},[582,1172,1173,1181],{},[585,1174,1175,1177,1179],{},[588,1176,993],{},[636,1178,939],{},[715,1180,942],{},[592,1182,1093],{"encoding":594},[569,1184,1186,1204],{"className":1185,"ariaHidden":599},[598],[569,1187,1189,1192,1195,1198,1201],{"className":1188},[603],[569,1190],{"className":1191,"style":1041},[607],[569,1193,993],{"className":1194,"style":1009},[612,613],[569,1196],{"className":1197,"style":806},[662],[569,1199,939],{"className":1200},[810],[569,1202],{"className":1203,"style":806},[662],[569,1205,1207,1210,1213,1219],{"className":1206},[603],[569,1208],{"className":1209,"style":955},[607],[569,1211,962],{"className":1212},[612],[569,1214,1216],{"className":1215},[612],[569,1217,970],{"className":1218},[969],[569,1220,974],{"className":1221},[612],". Weitere Fälle:",[1224,1225,1226,1655],"ul",{},[1227,1228,1229],"li",{},[569,1230,1232,1321],{"className":1231},[572],[569,1233,1235],{"className":1234},[576],[578,1236,1237],{"xmlns":580},[582,1238,1239,1318],{},[585,1240,1241,1244,1246,1249,1252,1255,1257,1260,1262,1265,1269,1292,1294,1296],{},[588,1242,1243],{},"P",[636,1245,713],{"stretchy":712},[588,1247,1248],{},"a",[636,1250,1251],{},"≤",[588,1253,1254],{},"X",[636,1256,1251],{},[588,1258,1259],{},"b",[636,1261,725],{"stretchy":712},[636,1263,1264],{},"≈",[588,1266,1268],{"mathvariant":1267},"normal","Φ",[585,1270,1271,1273,1290],{},[636,1272,713],{"fence":599},[1274,1275,1276,1288],"mfrac",{},[585,1277,1278,1280,1282,1284,1286],{},[588,1279,1259],{},[636,1281,939],{},[715,1283,942],{},[636,1285,720],{},[588,1287,634],{},[588,1289,698],{},[636,1291,725],{"fence":599},[636,1293,720],{},[588,1295,1268],{"mathvariant":1267},[585,1297,1298,1300,1316],{},[636,1299,713],{"fence":599},[1274,1301,1302,1314],{},[585,1303,1304,1306,1308,1310,1312],{},[588,1305,1248],{},[636,1307,720],{},[715,1309,942],{},[636,1311,720],{},[588,1313,634],{},[588,1315,698],{},[636,1317,725],{"fence":599},[592,1319,1320],{"encoding":594},"P(a \\leq X \\leq b) \\approx \\Phi\\left(\\frac{b + 0{,}5 - \\mu}{\\sigma}\\right) - \\Phi\\left(\\frac{a - 0{,}5 - \\mu}{\\sigma}\\right)",[569,1322,1324,1350,1370,1391,1536],{"className":1323,"ariaHidden":599},[598],[569,1325,1327,1331,1335,1338,1341,1344,1347],{"className":1326},[603],[569,1328],{"className":1329,"style":1330},[607],"height:1em;vertical-align:-0.25em;",[569,1332,1243],{"className":1333,"style":1334},[612,613],"margin-right:0.1389em;",[569,1336,713],{"className":1337},[799],[569,1339,1248],{"className":1340},[612,613],[569,1342],{"className":1343,"style":663},[662],[569,1345,1251],{"className":1346},[667],[569,1348],{"className":1349,"style":663},[662],[569,1351,1353,1357,1361,1364,1367],{"className":1352},[603],[569,1354],{"className":1355,"style":1356},[607],"height:0.8193em;vertical-align:-0.136em;",[569,1358,1254],{"className":1359,"style":1360},[612,613],"margin-right:0.0785em;",[569,1362],{"className":1363,"style":663},[662],[569,1365,1251],{"className":1366},[667],[569,1368],{"className":1369,"style":663},[662],[569,1371,1373,1376,1379,1382,1385,1388],{"className":1372},[603],[569,1374],{"className":1375,"style":1330},[607],[569,1377,1259],{"className":1378},[612,613],[569,1380,725],{"className":1381},[820],[569,1383],{"className":1384,"style":663},[662],[569,1386,1264],{"className":1387},[667],[569,1389],{"className":1390,"style":663},[662],[569,1392,1394,1398,1401,1405,1527,1530,1533],{"className":1393},[603],[569,1395],{"className":1396,"style":1397},[607],"height:1.8em;vertical-align:-0.65em;",[569,1399,1268],{"className":1400},[612],[569,1402],{"className":1403,"style":1404},[662],"margin-right:0.1667em;",[569,1406,1409,1419,1521],{"className":1407},[1408],"minner",[569,1410,1414],{"className":1411,"style":1413},[799,1412],"delimcenter","top:0em;",[569,1415,713],{"className":1416},[1417,1418],"delimsizing","size2",[569,1420,1422,1426,1518],{"className":1421},[612],[569,1423],{"className":1424},[799,1425],"nulldelimiter",[569,1427,1429],{"className":1428},[1274],[569,1430,1432,1509],{"className":1431},[765,766],[569,1433,1435,1506],{"className":1434},[770],[569,1436,1439,1459,1470],{"className":1437,"style":1438},[774],"height:0.9322em;",[569,1440,1442,1446],{"style":1441},"top:-2.655em;",[569,1443],{"className":1444,"style":1445},[784],"height:3em;",[569,1447,1453],{"className":1448},[1449,1450,1451,1452],"sizing","reset-size6","size3","mtight",[569,1454,1456],{"className":1455},[612,1452],[569,1457,698],{"className":1458,"style":741},[612,613,1452],[569,1460,1462,1465],{"style":1461},"top:-3.23em;",[569,1463],{"className":1464,"style":1445},[784],[569,1466],{"className":1467,"style":1469},[1468],"frac-line","border-bottom-width:0.04em;",[569,1471,1473,1476],{"style":1472},"top:-3.4461em;",[569,1474],{"className":1475,"style":1445},[784],[569,1477,1479],{"className":1478},[1449,1450,1451,1452],[569,1480,1482,1485,1488,1491,1497,1500,1503],{"className":1481},[612,1452],[569,1483,1259],{"className":1484},[612,613,1452],[569,1486,939],{"className":1487},[810,1452],[569,1489,962],{"className":1490},[612,1452],[569,1492,1494],{"className":1493},[612,1452],[569,1495,970],{"className":1496},[969,1452],[569,1498,974],{"className":1499},[612,1452],[569,1501,720],{"className":1502},[810,1452],[569,1504,634],{"className":1505},[612,613,1452],[569,1507,848],{"className":1508},[847],[569,1510,1512],{"className":1511},[770],[569,1513,1516],{"className":1514,"style":1515},[774],"height:0.345em;",[569,1517],{},[569,1519],{"className":1520},[820,1425],[569,1522,1524],{"className":1523,"style":1413},[820,1412],[569,1525,725],{"className":1526},[1417,1418],[569,1528],{"className":1529,"style":806},[662],[569,1531,720],{"className":1532},[810],[569,1534],{"className":1535,"style":806},[662],[569,1537,1539,1543,1546,1549],{"className":1538},[603],[569,1540],{"className":1541,"style":1542},[607],"height:1.2472em;vertical-align:-0.35em;",[569,1544,1268],{"className":1545},[612],[569,1547],{"className":1548,"style":1404},[662],[569,1550,1552,1559,1649],{"className":1551},[1408],[569,1553,1555],{"className":1554,"style":1413},[799,1412],[569,1556,713],{"className":1557},[1417,1558],"size1",[569,1560,1562,1565,1646],{"className":1561},[612],[569,1563],{"className":1564},[799,1425],[569,1566,1568],{"className":1567},[1274],[569,1569,1571,1638],{"className":1570},[765,766],[569,1572,1574,1635],{"className":1573},[770],[569,1575,1578,1592,1600],{"className":1576,"style":1577},[774],"height:0.8972em;",[569,1579,1580,1583],{"style":1441},[569,1581],{"className":1582,"style":1445},[784],[569,1584,1586],{"className":1585},[1449,1450,1451,1452],[569,1587,1589],{"className":1588},[612,1452],[569,1590,698],{"className":1591,"style":741},[612,613,1452],[569,1593,1594,1597],{"style":1461},[569,1595],{"className":1596,"style":1445},[784],[569,1598],{"className":1599,"style":1469},[1468],[569,1601,1602,1605],{"style":1472},[569,1603],{"className":1604,"style":1445},[784],[569,1606,1608],{"className":1607},[1449,1450,1451,1452],[569,1609,1611,1614,1617,1620,1626,1629,1632],{"className":1610},[612,1452],[569,1612,1248],{"className"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Näherung für einen einzelnen Wert: ",[569,1662,1664,1717],{"className":1663},[572],[569,1665,1667],{"className":1666},[576],[578,1668,1669],{"xmlns":580},[582,1670,1671,1714],{},[585,1672,1673,1675,1677,1679,1681,1683,1685,1687,1693,1696],{},[588,1674,1243],{},[636,1676,713],{"stretchy":712},[588,1678,1254],{},[636,1680,638],{},[588,1682,993],{},[636,1684,725],{"stretchy":712},[636,1686,1264],{},[1274,1688,1689,1691],{},[715,1690,717],{},[588,1692,698],{},[588,1694,1695],{},"φ",[585,1697,1698,1700,1712],{},[636,1699,713],{"fence":599},[1274,1701,1702,1710],{},[585,1703,1704,1706,1708],{},[588,1705,993],{},[636,1707,720],{},[588,1709,634],{},[588,1711,698],{},[636,1713,725],{"fence":599},[592,1715,1716],{"encoding":594},"P(X = k) \\approx \\frac{1}{\\sigma} \\varphi\\left(\\frac{k - \\mu}{\\sigma}\\right)",[569,1718,1720,1744,1765],{"className":1719,"ariaHidden":599},[598],[569,1721,1723,1726,1729,1732,1735,1738,1741],{"className":1722},[603],[569,1724],{"className":1725,"style":1330},[607],[569,1727,1243],{"className":1728,"style":1334},[612,613],[569,1730,713],{"className":1731},[799],[569,1733,1254],{"className":1734,"style":1360},[612,613],[569,1736],{"className":1737,"style":663},[662],[569,1739,638],{"className":1740},[667],[569,1742],{"className":1743,"style":663},[662],[569,1745,1747,1750,1753,1756,1759,1762],{"className":1746},[603],[569,1748],{"className":1749,"style":1330},[607],[569,1751,993],{"className":1752,"style":1009},[612,613],[569,1754,725],{"className":1755},[820],[569,1757],{"className":1758,"style":663},[662],[569,1760,1264],{"className":1761},[667],[569,1763],{"className":1764,"style":663},[662],[569,1766,1768,1771,1841,1844,1847],{"className":1767},[603],[569,1769],{"className":1770,"style":1397},[607],[569,1772,1774,1777,1838],{"className":1773},[612],[569,1775],{"className":1776},[799,1425],[569,1778,1780],{"className":1779},[1274],[569,1781,1783,1830],{"className":1782},[765,766],[569,1784,1786,1827],{"className":1785},[770],[569,1787,1790,1804,1812],{"className":1788,"style":1789},[774],"height:0.8451em;",[569,1791,1792,1795],{"style":1441},[569,1793],{"className":1794,"style":1445},[784],[569,1796,1798],{"className":1797},[1449,1450,1451,1452],[569,1799,1801],{"className":1800},[612,1452],[569,1802,698],{"className":1803,"style":741},[612,613,1452],[569,1805,1806,1809],{"style":1461},[569,1807],{"className":1808,"style":1445},[784],[569,1810],{"className":1811,"style":1469},[1468],[569,1813,1815,1818],{"style":1814},"top:-3.394em;",[569,1816],{"className":1817,"style":1445},[784],[569,1819,1821],{"className":1820},[1449,1450,1451,1452],[569,1822,1824],{"className":1823},[612,1452],[569,1825,717],{"className":1826},[612,1452],[569,1828,848],{"className":1829},[847],[569,1831,1833],{"className":1832},[770],[569,1834,1836],{"className":1835,"style":1515},[774],[569,1837],{},[569,1839],{"className":1840},[820,1425],[569,1842,1695],{"className":1843},[612,613],[569,1845],{"className":1846,"style":1404},[662],[569,1848,1850,1856,1930],{"className":1849},[1408],[569,1851,1853],{"className":1852,"style":1413},[799,1412],[569,1854,713],{"className":1855},[1417,1418],[569,1857,1859,1862,1927],{"className":1858},[612],[569,1860],{"className":1861},[799,1425],[569,1863,1865],{"className":1864},[1274],[569,1866,1868,1919],{"className":1867},[765,766],[569,1869,1871,1916],{"className":1870},[770],[569,1872,1874,1888,1896],{"className":1873,"style":1438},[774],[569,1875,1876,1879],{"style":1441},[569,1877],{"className":1878,"style":1445},[784],[569,1880,1882],{"className":1881},[1449,1450,1451,1452],[569,1883,1885],{"className":1884},[612,1452],[569,1886,698],{"className":1887,"style":741},[612,613,1452],[569,1889,1890,1893],{"style":1461},[569,1891],{"className":1892,"style":1445},[784],[569,1894],{"className":1895,"style":1469},[1468],[569,1897,1898,1901],{"style":1472},[569,1899],{"className":1900,"style":1445},[784],[569,1902,1904],{"className":1903},[1449,1450,1451,1452],[569,1905,1907,1910,1913],{"className":1906},[612,1452],[569,1908,993],{"className":1909,"style":1009},[612,613,1452],[569,1911,720],{"className":1912},[810,1452],[569,1914,634],{"className":1915},[612,613,1452],[569,1917,848],{"className":1918},[847],[569,1920,1922],{"className":1921},[770],[569,1923,1925],{"className":1924,"style":1515},[774],[569,1926],{},[569,1928],{"className":1929},[820,1425],[569,1931,1933],{"className":1932,"style":1413},[820,1412],[569,1934,725],{"className":1935},[1417,1418]," mit der Dichte ",[569,1938,1940,1954],{"className":1939},[572],[569,1941,1943],{"className":1942},[576],[578,1944,1945],{"xmlns":580},[582,1946,1947,1951],{},[585,1948,1949],{},[588,1950,1695],{},[592,1952,1953],{"encoding":594},"\\varphi",[569,1955,1957],{"className":1956,"ariaHidden":599},[598],[569,1958,1960,1963],{"className":1959},[603],[569,1961],{"className":1962,"style":655},[607],[569,1964,1695],{"className":1965},[612,613]," der Standardnormalverteilung.",[565,1968,1969],{},"Heute rechnen Taschenrechner Binomialwahrscheinlichkeiten meist direkt. Die Näherung bleibt wichtig, weil sie die Sigma-Regeln und Konfidenzintervalle begründet.",[560,1971,1973],{"id":1972},"beispiele","Beispiele",[565,1975,1976,1977,2006,2007,2036,2037,2143,2144,2348,2349,2378],{},"Eine faire Münze wird ",[569,1978,1980,1994],{"className":1979},[572],[569,1981,1983],{"className":1982},[576],[578,1984,1985],{"xmlns":580},[582,1986,1987,1992],{},[585,1988,1989],{},[715,1990,1991],{},"100",[592,1993,1991],{"encoding":594},[569,1995,1997],{"className":1996,"ariaHidden":599},[598],[569,1998,2000,2003],{"className":1999},[603],[569,2001],{"className":2002,"style":917},[607],[569,2004,1991],{"className":2005},[612],"-mal geworfen, ",[569,2008,2010,2023],{"className":2009},[572],[569,2011,2013],{"className":2012},[576],[578,2014,2015],{"xmlns":580},[582,2016,2017,2021],{},[585,2018,2019],{},[588,2020,1254],{},[592,2022,1254],{"encoding":594},[569,2024,2026],{"className":2025,"ariaHidden":599},[598],[569,2027,2029,2033],{"className":2028},[603],[569,2030],{"className":2031,"style":2032},[607],"height:0.6833em;",[569,2034,1254],{"className":2035,"style":1360},[612,613]," ist die Anzahl „Kopf“. Dann ist ",[569,2038,2040,2068],{"className":2039},[572],[569,2041,2043],{"className":2042},[576],[578,2044,2045],{"xmlns":580},[582,2046,2047,2065],{},[585,2048,2049,2051,2053,2055,2058,2060,2062],{},[588,2050,634],{},[636,2052,638],{},[715,2054,1991],{},[636,2056,2057],{},"⋅",[715,2059,942],{},[636,2061,638],{},[715,2063,2064],{},"50",[592,2066,2067],{"encoding":594},"\\mu = 100 \\cdot 0{,}5 = 50",[569,2069,2071,2089,2107,2134],{"className":2070,"ariaHidden":599},[598],[569,2072,2074,2077,2080,2083,2086],{"className":2073},[603],[569,2075],{"className":2076,"style":655},[607],[569,2078,634],{"className":2079},[612,613],[569,2081],{"className":2082,"style":663},[662],[569,2084,638],{"className":2085},[667],[569,2087],{"className":2088,"style":663},[662],[569,2090,2092,2095,2098,2101,2104],{"className":2091},[603],[569,2093],{"className":2094,"style":917},[607],[569,2096,1991],{"className":2097},[612],[569,2099],{"className":2100,"style":806},[662],[569,2102,2057],{"className":2103},[810],[569,2105],{"className":2106,"style":806},[662],[569,2108,2110,2113,2116,2122,2125,2128,2131],{"className":2109},[603],[569,2111],{"className":2112,"style":955},[607],[569,2114,962],{"className":2115},[612],[569,2117,2119],{"className":2118},[612],[569,2120,970],{"className":2121},[969],[569,2123,974],{"className":2124},[612],[569,2126],{"className":2127,"style":663},[662],[569,2129,638],{"className":2130},[667],[569,2132],{"className":2133,"style":663},[662],[569,2135,2137,2140],{"className":2136},[603],[569,2138],{"className":2139,"style":917},[607],[569,2141,2064],{"className":2142},[612]," und ",[569,2145,2147,2185],{"className":2146},[572],[569,2148,2150],{"className":2149},[576],[578,2151,2152],{"xmlns":580},[582,2153,2154,2182],{},[585,2155,2156,2158,2160,2174,2176,2178,2180],{},[588,2157,698],{},[636,2159,638],{},[702,2161,2162],{},[585,2163,2164,2166,2168,2170,2172],{},[715,2165,1991],{},[636,2167,2057],{},[715,2169,942],{},[636,2171,2057],{},[715,2173,942],{},[636,2175,638],{},[715,2177,974],{},[636,2179,882],{},[715,2181,885],{},[592,2183,2184],{"encoding":594},"\\sigma = \\sqrt{100 \\cdot 0{,}5 \\cdot 0{,}5} = 5 > 3",[569,2186,2188,2206,2320,2339],{"className":2187,"ariaHidden":599},[598],[569,2189,2191,2194,2197,2200,2203],{"className":2190},[603],[569,2192],{"className":2193,"style":608},[607],[569,2195,698],{"className":2196,"style":741},[612,613],[569,2198],{"className":2199,"style":663},[662],[569,2201,638],{"className":2202},[667],[569,2204],{"className":2205,"style":663},[662],[569,2207,2209,2213,2311,2314,2317],{"className":2208},[603],[569,2210],{"className":2211,"style":2212},[607],"height:1.04em;vertical-align:-0.23em;",[569,2214,2216],{"className":2215},[612,761],[569,2217,2219,2302],{"className":2218},[765,766],[569,2220,2222,2299],{"className":2221},[770],[569,2223,2226,2282],{"className":2224,"style":2225},[774],"height:0.81em;",[569,2227,2230,2233],{"className":2228,"style":2229},[779],"top:-3em;",[569,2231],{"className":2232,"style":1445},[784],[569,2234,2237,2240,2243,2246,2249,2252,2258,2261,2264,2267,2270,2273,2279],{"className":2235,"style":2236},[612],"padding-left:0.833em;",[569,2238,1991],{"className":2239},[612],[569,2241],{"className":2242,"style":806},[662],[569,2244,2057],{"className":2245},[810],[569,2247],{"className":2248,"style":806},[662],[569,2250,962],{"className":2251},[612],[569,2253,2255],{"className":2254},[612],[569,2256,970],{"className":2257},[969],[569,2259,974],{"className":2260},[612],[569,2262],{"className":2263,"style":806},[662],[569,2265,2057],{"className":2266},[810],[569,2268],{"className":2269,"style":806},[662],[569,2271,962],{"className":2272},[612],[569,2274,2276],{"className":2275},[612],[569,2277,970],{"className":2278},[969],[569,2280,974],{"className":2281},[612],[569,2283,2285,2288],{"style":2284},"top:-2.77em;",[569,2286],{"className":2287,"style":1445},[784],[569,2289,2292],{"className":2290,"style":2291},[830],"min-width:0.853em;height:1.08em;",[833,2293,2296],{"xmlns":835,"width":836,"height":2294,"viewBox":2295,"preserveAspectRatio":839},"1.08em","0 0 400000 1080",[841,2297],{"d":2298},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[569,2300,848],{"className":2301},[847],[569,2303,2305],{"className":2304},[770],[569,2306,2309],{"className":2307,"style":2308},[774],"height:0.23em;",[569,2310],{},[569,2312],{"className":2313,"style":663},[662],[569,2315,638],{"className":2316},[667],[569,2318],{"className":2319,"style":663},[662],[569,2321,2323,2327,2330,2333,2336],{"className":2322},[603],[569,2324],{"className":2325,"style":2326},[607],"height:0.6835em;vertical-align:-0.0391em;",[569,2328,974],{"className":2329},[612],[569,2331],{"className":2332,"style":663},[662],[569,2334,882],{"className":2335},[667],[569,2337],{"className":2338,"style":663},[662],[569,2340,2342,2345],{"className":2341},[603],[569,2343],{"className":2344,"style":917},[607],[569,2346,885],{"className":2347},[612],". Höchstens ",[569,2350,2352,2366],{"className":2351},[572],[569,2353,2355],{"className":2354},[576],[578,2356,2357],{"xmlns":580},[582,2358,2359,2364],{},[585,2360,2361],{},[715,2362,2363],{},"55",[592,2365,2363],{"encoding":594},[569,2367,2369],{"className":2368,"ariaHidden":599},[598],[569,2370,2372,2375],{"className":2371},[603],[569,2373],{"className":2374,"style":917},[607],[569,2376,2363],{"className":2377},[612],"-mal Kopf:",[569,2380,2383],{"className":2381},[2382],"katex-display",[569,2384,2386,2453],{"className":2385},[572],[569,2387,2389],{"className":2388},[576],[578,2390,2392],{"xmlns":580,"display":2391},"block",[582,2393,2394,2450],{},[585,2395,2396,2398,2400,2402,2404,2406,2408,2410,2412,2434,2436,2438,2440,2443,2445,2447],{},[588,2397,1243],{},[636,2399,713],{"stretchy":712},[588,2401,1254],{},[636,2403,1251],{},[715,2405,2363],{},[636,2407,725],{"stretchy":712},[636,2409,1264],{},[588,2411,1268],{"mathvariant":1267},[585,2413,2414,2416,2432],{},[636,2415,713],{"fence":599},[1274,2417,2418,2430],{},[585,2419,2420,2422,2424,2426,2428],{},[715,2421,2363],{},[636,2423,939],{},[715,2425,942],{},[636,2427,720],{},[715,2429,2064],{},[715,2431,974],{},[636,2433,725],{"fence":599},[636,2435,638],{},[588,2437,1268],{"mathvariant":1267},[636,2439,713],{"stretchy":712},[715,2441,2442],{},"1,1",[636,2444,725],{"stretchy":712},[636,2446,1264],{},[715,2448,2449],{},"0,8643",[592,2451,2452],{"encoding":594},"P(X \\leq 55) \\approx \\Phi\\left(\\frac{55 + 0{,}5 - 50}{5}\\right) = \\Phi(1{,}1) \\approx 0{,}8643",[569,2454,2456,2480,2501,2637,2673],{"className":2455,"ariaHidden":599},[598],[569,2457,2459,2462,2465,2468,2471,2474,2477],{"className":2458},[603],[569,2460],{"className":2461,"style":1330},[607],[569,2463,1243],{"className":2464,"style":1334},[612,613],[569,2466,713],{"className":2467},[799],[569,2469,1254],{"className":2470,"style":1360},[612,613],[569,2472],{"className":2473,"style":663},[662],[569,2475,1251],{"className":2476},[667],[569,2478],{"className":2479,"style":663},[662],[569,2481,2483,2486,2489,2492,2495,2498],{"className":2482},[603],[569,2484],{"className":2485,"style":1330},[607],[569,2487,2363],{"className":2488},[612],[569,2490,725],{"className":2491},[820],[569,2493],{"className":2494,"style":663},[662],[569,2496,1264],{"className":2497},[667],[569,2499],{"className":2500,"style":663},[662],[569,2502,2504,2508,2511,2514,2628,2631,2634],{"className":2503},[603],[569,2505],{"className":2506,"style":2507},[607],"height:2.4em;vertical-align:-0.95em;",[569,2509,1268],{"className":2510},[612],[569,2512],{"className":2513,"style":1404},[662],[569,2515,2517,2523,2622],{"className":2516},[1408],[569,2518,2520],{"className":2519,"style":1413},[799,1412],[569,2521,713],{"className":2522},[1417,1451],[569,2524,2526,2529,2619],{"className":2525},[612],[569,2527],{"className":2528},[799,1425],[569,2530,2532],{"className":2531},[1274],[569,2533,2535,2610],{"className":2534},[765,766],[569,2536,2538,2607],{"className":2537},[770],[569,2539,2542,2554,2562],{"className":2540,"style":2541},[774],"height:1.3214em;",[569,2543,2545,2548],{"style":2544},"top:-2.314em;",[569,2546],{"className":2547,"style":1445},[784],[569,2549,2551],{"className":2550},[612],[569,2552,974],{"className":2553},[612],[569,2555,2556,2559],{"style":1461},[569,2557],{"className":2558,"style":1445},[784],[569,2560],{"className":2561,"style":1469},[1468],[569,2563,2565,2568],{"style":2564},"top:-3.677em;",[569,2566],{"className":2567,"style":1445},[784],[569,2569,2571,2574,2577,2580,2583,2586,2592,2595,2598,2601,2604],{"className":2570},[612],[569,2572,2363],{"className":2573},[612],[569,2575],{"className":2576,"style":806},[662],[569,2578,939],{"className":2579},[810],[569,2581],{"className":2582,"style":806},[662],[569,2584,962],{"className":2585},[612],[569,2587,2589],{"className":2588},[612],[569,2590,970],{"className":2591},[969],[569,2593,974],{"className":2594},[612],[569,2596],{"className":2597,"style":806},[662],[569,2599,720],{"className":2600},[810],[569,2602],{"className":2603,"style":806},[662],[569,2605,2064],{"className":2606},[612],[569,2608,848],{"className":2609},[847],[569,2611,2613],{"className":2612},[770],[569,2614,2617],{"className":2615,"style":2616},[774],"height:0.686em;",[569,2618],{},[569,2620],{"className":2621},[820,1425],[569,2623,2625],{"className":2624,"style":1413},[820,1412],[569,2626,725],{"className":2627},[1417,1451],[569,2629],{"className":2630,"style":663},[662],[569,2632,638],{"className":2633},[667],[569,2635],{"className":2636,"style":663},[662],[569,2638,2640,2643,2646,2649,2652,2658,2661,2664,2667,2670],{"className":2639},[603],[569,2641],{"className":2642,"style":1330},[607],[569,2644,1268],{"className":2645},[612],[569,2647,713],{"className":2648},[799],[569,2650,717],{"className":2651},[612],[569,2653,2655],{"className":2654},[612],[569,2656,970],{"className":2657},[969],[569,2659,717],{"className":2660},[612],[569,2662,725],{"className":2663},[820],[569,2665],{"className":2666,"style":663},[662],[569,2668,1264],{"className":2669},[667],[569,2671],{"className":2672,"style":663},[662],[569,2674,2676,2679,2682,2688],{"className":2675},[603],[569,2677],{"className":2678,"style":955},[607],[569,2680,962],{"className":2681},[612],[569,2683,2685],{"className":2684},[612],[569,2686,970],{"className":2687},[969],[569,2689,2691],{"className":2690},[612],"8643",[565,2693,2694,2695,2735,2736,2813],{},"Der exakte Wert ist ",[569,2696,2698,2713],{"className":2697},[572],[569,2699,2701],{"className":2700},[576],[578,2702,2703],{"xmlns":580},[582,2704,2705,2710],{},[585,2706,2707],{},[715,2708,2709],{},"0,8644",[592,2711,2712],{"encoding":594},"0{,}8644",[569,2714,2716],{"className":2715,"ariaHidden":599},[598],[569,2717,2719,2722,2725,2731],{"className":2718},[603],[569,2720],{"className":2721,"style":955},[607],[569,2723,962],{"className":2724},[612],[569,2726,2728],{"className":2727},[612],[569,2729,970],{"className":2730},[969],[569,2732,2734],{"className":2733},[612],"8644",". Ohne Stetigkeitskorrektur erhielte man nur ",[569,2737,2739,2764],{"className":2738},[572],[569,2740,2742],{"className":2741},[576],[578,2743,2744],{"xmlns":580},[582,2745,2746,2761],{},[585,2747,2748,2750,2752,2754,2756,2758],{},[588,2749,1268],{"mathvariant":1267},[636,2751,713],{"stretchy":712},[715,2753,717],{},[636,2755,725],{"stretchy":712},[636,2757,1264],{},[715,2759,2760],{},"0,8413",[592,2762,2763],{"encoding":594},"\\Phi(1) \\approx 0{,}8413",[569,2765,2767,2794],{"className":2766,"ariaHidden":599},[598],[569,2768,2770,2773,2776,2779,2782,2785,2788,2791],{"className":2769},[603],[569,2771],{"className":2772,"style":1330},[607],[569,2774,1268],{"className":2775},[612],[569,2777,713],{"className":2778},[799],[569,2780,717],{"className":2781},[612],[569,2783,725],{"className":2784},[820],[569,2786],{"className":2787,"style":663},[662],[569,2789,1264],{"className":2790},[667],[569,2792],{"className":2793,"style":663},[662],[569,2795,2797,2800,2803,2809],{"className":2796},[603],[569,2798],{"className":2799,"style":955},[607],[569,2801,962],{"className":2802},[612],[569,2804,2806],{"className":2805},[612],[569,2807,970],{"className":2808},[969],[569,2810,2812],{"className":2811},[612],"8413",".",[565,2815,2816,2817,2378],{},"Lokale Näherung für genau ",[569,2818,2820,2833],{"className":2819},[572],[569,2821,2823],{"className":2822},[576],[578,2824,2825],{"xmlns":580},[582,2826,2827,2831],{},[585,2828,2829],{},[715,2830,2064],{},[592,2832,2064],{"encoding":594},[569,2834,2836],{"className":2835,"ariaHidden":599},[598],[569,2837,2839,2842],{"className":2838},[603],[569,2840],{"className":2841,"style":917},[607],[569,2843,2064],{"className":2844},[612],[569,2846,2848],{"className":2847},[2382],[569,2849,2851,2904],{"className":2850},[572],[569,2852,2854],{"className":2853},[576],[578,2855,2856],{"xmlns":580,"display":2391},[582,2857,2858,2901],{},[585,2859,2860,2862,2864,2866,2868,2870,2872,2874,2880,2882,2896,2898],{},[588,2861,1243],{},[636,2863,713],{"stretchy":712},[588,2865,1254],{},[636,2867,638],{},[715,2869,2064],{},[636,2871,725],{"stretchy":712},[636,2873,1264],{},[1274,2875,2876,2878],{},[715,2877,717],{},[715,2879,974],{},[636,2881,2057],{},[1274,2883,2884,2886],{},[715,2885,717],{},[702,2887,2888],{},[585,2889,2890,2893],{},[715,2891,2892],{},"2",[588,2894,2895],{},"π",[636,2897,1264],{},[715,2899,2900],{},"0,0798",[592,2902,2903],{"encoding":594},"P(X = 50) \\approx \\frac{1}{5} \\cdot \\frac{1}{\\sqrt{2\\pi}} \\approx 0{,}0798",[569,2905,2907,2931,2952,3030,3160],{"className":2906,"ariaHidden":599},[598],[569,2908,2910,2913,2916,2919,2922,2925,2928],{"className":2909},[603],[569,2911],{"className":2912,"style":1330},[607],[569,2914,1243],{"className":2915,"style":1334},[612,613],[569,2917,713],{"className":2918},[799],[569,2920,1254],{"className":2921,"style":1360},[612,613],[569,2923],{"className":2924,"style":663},[662],[569,2926,638],{"className":2927},[667],[569,2929],{"className":2930,"style":663},[662],[569,2932,2934,2937,2940,2943,2946,2949],{"className":2933},[603],[569,2935],{"className":2936,"style":1330},[607],[569,2938,2064],{"className":2939},[612],[569,2941,725],{"className":2942},[820],[569,2944],{"className":2945,"style":663},[662],[569,2947,1264],{"className":2948},[667],[569,2950],{"className":2951,"style":663},[662],[569,2953,2955,2959,3021,3024,3027],{"className":2954},[603],[569,2956],{"className":2957,"style":2958},[607],"height:2.0074em;vertical-align:-0.686em;",[569,2960,2962,2965,3018],{"className":2961},[612],[569,2963],{"className":2964},[799,1425],[569,2966,2968],{"className":2967},[1274],[569,2969,2971,3010],{"className":2970},[765,766],[569,2972,2974,3007],{"className":2973},[770],[569,2975,2977,2988,2996],{"className":2976,"style":2541},[774],[569,2978,2979,2982],{"style":2544},[569,2980],{"className":2981,"style":1445},[784],[569,2983,2985],{"className":2984},[612],[569,2986,974],{"className":2987},[612],[569,2989,2990,2993],{"style":1461},[569,2991],{"className":2992,"style":1445},[784],[569,2994],{"className":2995,"style":1469},[1468],[569,2997,2998,3001],{"style":2564},[569,2999],{"className":3000,"style":1445},[784],[569,3002,3004],{"className":3003},[612],[569,3005,717],{"className":3006},[612],[569,3008,848],{"className":3009},[847],[569,3011,3013],{"className":3012},[770],[569,3014,3016],{"className":3015,"style":2616},[774],[569,3017],{},[569,3019],{"className":3020},[820,1425],[569,3022],{"className":3023,"style":806},[662],[569,3025,2057],{"className":3026},[810],[569,3028],{"className":3029,"style":806},[662],[569,3031,3033,3037,3151,3154,3157],{"className":3032},[603],[569,3034],{"className":3035,"style":3036},[607],"height:2.2514em;vertical-align:-0.93em;",[569,3038,3040,3043,3148],{"className":3039},[612],[569,3041],{"className":3042},[799,1425],[569,3044,3046],{"className":3045},[1274],[569,3047,3049,3139],{"className":3048},[765,766],[569,3050,3052,3136],{"className":3051},[770],[569,3053,3055,3117,3125],{"className":3054,"style":2541},[774],[569,3056,3058,3061],{"style":3057},"top:-2.2028em;",[569,3059],{"className":3060,"style":1445},[784],[569,3062,3064],{"className":3063},[612],[569,3065,3067],{"className":3066},[612,761],[569,3068,3070,3108],{"className":3069},[765,766],[569,3071,3073,3105],{"className":3072},[770],[569,3074,3077,3092],{"className":3075,"style":3076},[774],"height:0.9072em;",[569,3078,3080,3083],{"className":3079,"style":2229},[779],[569,3081],{"className":3082,"style":1445},[784],[569,3084,3086,3089],{"className":3085,"style":2236},[612],[569,3087,2892],{"className":3088},[612],[569,3090,2895],{"className":3091,"style":741},[612,613],[569,3093,3095,3098],{"style":3094},"top:-2.8672em;",[569,3096],{"className":3097,"style":1445},[784],[569,3099,3101],{"className":3100,"style":2291},[830],[833,3102,3103],{"xmlns":835,"width":836,"height":2294,"viewBox":2295,"preserveAspectRatio":839},[841,3104],{"d":2298},[569,3106,848],{"className":3107},[847],[569,3109,3111],{"className":3110},[770],[569,3112,3115],{"className":3113,"style":3114},[774],"height:0.1328em;",[569,3116],{},[569,3118,3119,3122],{"style":1461},[569,3120],{"className":3121,"style":1445},[784],[569,3123],{"className":3124,"style":1469},[1468],[569,3126,3127,3130],{"style":2564},[569,3128],{"className":3129,"style":1445},[784],[569,3131,3133],{"className":3132},[612],[569,3134,717],{"className":3135},[612],[569,3137,848],{"className":3138},[847],[569,3140,3142],{"className":3141},[770],[569,3143,3146],{"className":3144,"style":3145},[774],"height:0.93em;",[569,3147],{},[569,3149],{"className":3150},[820,1425],[569,3152],{"className":3153,"style":663},[662],[569,3155,1264],{"className":3156},[667],[569,3158],{"className":3159,"style":663},[662],[569,3161,3163,3166,3169,3175],{"className":3162},[603],[569,3164],{"className":3165,"style":955},[607],[569,3167,962],{"className":3168},[612],[569,3170,3172],{"className":3171},[612],[569,3173,970],{"className":3174},[969],[569,3176,3178],{"className":3177},[612],"0798",[565,3180,3181,3182,2813],{},"Exakt ist ",[569,3183,3185,3224],{"className":3184},[572],[569,3186,3188],{"className":3187},[576],[578,3189,3190],{"xmlns":580},[582,3191,3192,3221],{},[585,3193,3194,3207,3209,3216,3218],{},[585,3195,3196,3198,3205],{},[636,3197,713],{"fence":599},[1274,3199,3201,3203],{"linethickness":3200},"0px",[715,3202,1991],{},[715,3204,2064],{},[636,3206,725],{"fence":599},[636,3208,2057],{},[3210,3211,3212,3214],"msup",{},[715,3213,942],{},[715,3215,1991],{},[636,3217,1264],{},[715,3219,3220],{},"0,0796",[592,3222,3223],{"encoding":594},"\\binom{100}{50} \\cdot 0{,}5^{100} \\approx 0{,}0796",[569,3225,3227,3313,3373],{"className":3226,"ariaHidden":599},[598],[569,3228,3230,3234,3304,3307,3310],{"className":3229},[603],[569,3231],{"className":3232,"style":3233},[607],"height:1.2451em;vertical-align:-0.35em;",[569,3235,3237,3243,3298],{"className":3236},[612],[569,3238,3240],{"className":3239,"style":1413},[799,1412],[569,3241,713],{"className":3242},[1417,1558],[569,3244,3246],{"className":3245},[1274],[569,3247,3249,3290],{"className":3248},[765,766],[569,3250,3252,3287],{"className":3251},[770],[569,3253,3256,3272],{"className":3254,"style":3255},[774],"height:0.8951em;",[569,3257,3259,3263],{"style":3258},"top:-2.355em;",[569,3260],{"className":3261,"style":3262},[784],"height:2.7em;",[569,3264,3266],{"className":3265},[1449,1450,1451,1452],[569,3267,3269],{"className":3268},[612,1452],[569,3270,2064],{"className":3271},[612,1452],[569,3273,3275,3278],{"style":3274},"top:-3.144em;",[569,3276],{"className":3277,"style":3262},[784],[569,3279,3281],{"className":3280},[1449,1450,1451,1452],[569,3282,3284],{"className":3283},[612,1452],[569,3285,1991],{"className":3286},[612,1452],[569,3288,848],{"className":3289},[847],[569,3291,3293],{"className":3292},[770],[569,3294,3296],{"className":3295,"style":1515},[774],[569,3297],{},[569,3299,3301],{"className":3300,"style":1413},[820,1412],[569,3302,725],{"className":3303},[1417,1558],[569,3305],{"className":3306,"style":806},[662],[569,3308,2057],{"className":3309},[810],[569,3311],{"className":3312,"style":806},[662],[569,3314,3316,3320,3323,3329,3364,3367,3370],{"className":3315},[603],[569,3317],{"className":3318,"style":3319},[607],"height:1.0085em;vertical-align:-0.1944em;",[569,3321,962],{"className":3322},[612],[569,3324,3326],{"className":3325},[612],[569,3327,970],{"className":3328},[969],[569,3330,3332,3335],{"className":3331},[612],[569,3333,974],{"className":3334},[612],[569,3336,3339],{"className":3337},[3338],"msupsub",[569,3340,3342],{"className":3341},[765],[569,3343,3345],{"className":3344},[770],[569,3346,3349],{"className":3347,"style":3348},[774],"height:0.8141em;",[569,3350,3352,3355],{"style":3351},"top:-3.063em;margin-right:0.05em;",[569,3353],{"className":3354,"style":3262},[784],[569,3356,3358],{"className":3357},[1449,1450,1451,1452],[569,3359,3361],{"className":3360},[612,1452],[569,3362,1991],{"className":3363},[612,1452],[569,3365],{"className":3366,"style":663},[662],[569,3368,1264],{"className":3369},[667],[569,3371],{"className":3372,"style":663},[662],[569,3374,3376,3379,3382,3388],{"className":3375},[603],[569,3377],{"className":3378,"style":955},[607],[569,3380,962],{"className":3381},[612],[569,3383,3385],{"className":3384},[612],[569,3386,970],{"className":3387},[969],[569,3389,3391],{"className":3390},[612],"0796",[560,3393,3395],{"id":3394},"typische-fehler","Typische Fehler",[1224,3397,3398,3518,3778],{},[1227,3399,3400,3401,3430,3431,3517],{},"Die Laplace-Bedingung nicht prüfen. Bei ",[569,3402,3404,3418],{"className":3403},[572],[569,3405,3407],{"className":3406},[576],[578,3408,3409],{"xmlns":580},[582,3410,3411,3416],{},[585,3412,3413],{},[715,3414,3415],{},"20",[592,3417,3415],{"encoding":594},[569,3419,3421],{"className":3420,"ariaHidden":599},[598],[569,3422,3424,3427],{"className":3423},[603],[569,3425],{"className":3426,"style":917},[607],[569,3428,3415],{"className":3429},[612]," Münzwürfen ist ",[569,3432,3434,3458],{"className":3433},[572],[569,3435,3437],{"className":3436},[576],[578,3438,3439],{"xmlns":580},[582,3440,3441,3455],{},[585,3442,3443,3445,3447,3450,3453],{},[588,3444,698],{},[636,3446,1264],{},[715,3448,3449],{},"2,24",[636,3451,3452],{},"\u003C",[715,3454,885],{},[592,3456,3457],{"encoding":594},"\\sigma \\approx 2{,}24 \u003C 3",[569,3459,3461,3480,3508],{"className":3460,"ariaHidden":599},[598],[569,3462,3464,3468,3471,3474,3477],{"className":3463},[603],[569,3465],{"className":3466,"style":3467},[607],"height:0.4831em;",[569,3469,698],{"className":3470,"style":741},[612,613],[569,3472],{"className":3473,"style":663},[662],[569,3475,1264],{"className":3476},[667],[569,3478],{"className":3479,"style":663},[662],[569,3481,3483,3486,3489,3495,3499,3502,3505],{"className":3482},[603],[569,3484],{"className":3485,"style":955},[607],[569,3487,2892],{"className":3488},[612],[569,3490,3492],{"className":3491},[612],[569,3493,970],{"className":3494},[969],[569,3496,3498],{"className":3497},[612],"24",[569,3500],{"className":3501,"style":663},[662],[569,3503,3452],{"className":3504},[667],[569,3506],{"className":3507,"style":663},[662],[569,3509,3511,3514],{"className":3510},[603],[569,3512],{"className":3513,"style":917},[607],[569,3515,885],{"className":3516},[612],", die Näherung ist dann zu ungenau.",[1227,3519,3520,3521,3588,3589,3650,3651,3717,3718,2813],{},"Die Stetigkeitskorrektur in die falsche Richtung anbringen. Bei ",[569,3522,3524,3549],{"className":3523},[572],[569,3525,3527],{"className":3526},[576],[578,3528,3529],{"xmlns":580},[582,3530,3531,3546],{},[585,3532,3533,3535,3537,3539,3542,3544],{},[588,3534,1243],{},[636,3536,713],{"stretchy":712},[588,3538,1254],{},[636,3540,3541],{},"≥",[588,3543,1248],{},[636,3545,725],{"stretchy":712},[592,3547,3548],{"encoding":594},"P(X \\geq a)",[569,3550,3552,3576],{"className":3551,"ariaHidden":599},[598],[569,3553,3555,3558,3561,3564,3567,3570,3573],{"className":3554},[603],[569,3556],{"className":3557,"style":1330},[607],[569,3559,1243],{"className":3560,"style":1334},[612,613],[569,3562,713],{"className":3563},[799],[569,3565,1254],{"className":3566,"style":1360},[612,613],[569,3568],{"className":3569,"style":663},[662],[569,3571,3541],{"className":3572},[667],[569,3574],{"className":3575,"style":663},[662],[569,3577,3579,3582,3585],{"className":3578},[603],[569,3580],{"className":3581,"style":1330},[607],[569,3583,1248],{"className":3584},[612,613],[569,3586,725],{"className":3587},[820]," rechnet man mit ",[569,3590,3592,3610],{"className":3591},[572],[569,3593,3595],{"className":3594},[576],[578,3596,3597],{"xmlns":580},[582,3598,3599,3607],{},[585,3600,3601,3603,3605],{},[588,3602,1248],{},[636,3604,720],{},[715,3606,942],{},[592,3608,3609],{"encoding":594},"a - 0{,}5",[569,3611,3613,3632],{"className":3612,"ariaHidden":599},[598],[569,3614,3616,3620,3623,3626,3629],{"className":3615},[603],[569,3617],{"className":3618,"style":3619},[607],"height:0.6667em;vertical-align:-0.0833em;",[569,3621,1248],{"className":3622},[612,613],[569,3624],{"className":3625,"style":806},[662],[569,3627,720],{"className":3628},[810],[569,3630],{"className":3631,"style":806},[662],[569,3633,3635,3638,3641,3647],{"className":3634},[603],[569,3636],{"className":3637,"style":955},[607],[569,3639,962],{"className":3640},[612],[569,3642,3644],{"className":3643},[612],[569,3645,970],{"className":3646},[969],[569,3648,974],{"className":3649},[612],", bei ",[569,3652,3654,3678],{"className":3653},[572],[569,3655,3657],{"className":3656},[576],[578,3658,3659],{"xmlns":580},[582,3660,3661,3675],{},[585,3662,3663,3665,3667,3669,3671,3673],{},[588,3664,1243],{},[636,3666,713],{"stretchy":712},[588,3668,1254],{},[636,3670,1251],{},[588,3672,1259],{},[636,3674,725],{"stretchy":712},[592,3676,3677],{"encoding":594},"P(X \\leq b)",[569,3679,3681,3705],{"className":3680,"ariaHidden":599},[598],[569,3682,3684,3687,3690,3693,3696,3699,3702],{"className":3683},[603],[569,3685],{"className":3686,"style":1330},[607],[569,3688,1243],{"className":3689,"style":1334},[612,613],[569,3691,713],{"className":3692},[799],[569,3694,1254],{"className":3695,"style":1360},[612,613],[569,3697],{"className":3698,"style":663},[662],[569,3700,1251],{"className":3701},[667],[569,3703],{"className":3704,"style":663},[662],[569,3706,3708,3711,3714],{"className":3707},[603],[569,3709],{"className":3710,"style":1330},[607],[569,3712,1259],{"className":3713},[612,613],[569,3715,725],{"className":3716},[820]," mit ",[569,3719,3721,3739],{"className":3720},[572],[569,3722,3724],{"className":3723},[576],[578,3725,3726],{"xmlns":580},[582,3727,3728,3736],{},[585,3729,3730,3732,3734],{},[588,3731,1259],{},[636,3733,939],{},[715,3735,942],{},[592,3737,3738],{"encoding":594},"b + 0{,}5",[569,3740,3742,3760],{"className":3741,"ariaHidden":599},[598],[569,3743,3745,3748,3751,3754,3757],{"className":3744},[603],[569,3746],{"className":3747,"style":1041},[607],[569,3749,1259],{"className":3750},[612,613],[569,3752],{"className":3753,"style":806},[662],[569,3755,939],{"className":3756},[810],[569,3758],{"className":3759,"style":806},[662],[569,3761,3763,3766,3769,3775],{"className":3762},[603],[569,3764],{"className":3765,"style":955},[607],[569,3767,962],{"className":3768},[612],[569,3770,3772],{"className":3771},[612],[569,3773,970],{"className":3774},[969],[569,3776,974],{"className":3777},[612],[1227,3779,3780,3781,3852,3853,3882],{},"Mit der Varianz ",[569,3782,3784,3810],{"className":3783},[572],[569,3785,3787],{"className":3786},[576],[578,3788,3789],{"xmlns":580},[582,3790,3791,3807],{},[585,3792,3793,3795,3797,3799,3801,3803,3805],{},[588,3794,590],{},[588,3796,565],{},[636,3798,713],{"stretchy":712},[715,3800,717],{},[636,3802,720],{},[588,3804,565],{},[636,3806,725],{"stretchy":712},[592,3808,3809],{"encoding":594},"np(1-p)",[569,3811,3813,3840],{"className":3812,"ariaHidden":599},[598],[569,3814,3816,3819,3822,3825,3828,3831,3834,3837],{"className":3815},[603],[569,3817],{"className":3818,"style":1330},[607],[569,3820,590],{"className":3821},[612,613],[569,3823,565],{"className":3824},[612,613],[569,3826,713],{"className":3827},[799],[569,3829,717],{"className":3830},[612],[569,3832],{"className":3833,"style":806},[662],[569,3835,720],{"className":3836},[810],[569,3838],{"className":3839,"style":806},[662],[569,3841,3843,3846,3849],{"className":3842},[603],[569,3844],{"className":3845,"style":1330},[607],[569,3847,565],{"className":3848},[612,613],[569,3850,725],{"className":3851},[820]," statt mit ",[569,3854,3856,3870],{"className":3855},[572],[569,3857,3859],{"className":3858},[576],[578,3860,3861],{"xmlns":580},[582,3862,3863,3867],{},[585,3864,3865],{},[588,3866,698],{},[592,3868,3869],{"encoding":594},"\\sigma",[569,3871,3873],{"className":3872,"ariaHidden":599},[598],[569,3874,3876,3879],{"className":3875},[603],[569,3877],{"className":3878,"style":608},[607],[569,3880,698],{"className":3881,"style":741},[612,613]," standardisieren.",{"title":3884,"searchDepth":3885,"depth":3885,"links":3886},"",2,[3887,3888,3889],{"id":562,"depth":3885,"text":563},{"id":1972,"depth":3885,"text":1973},{"id":3394,"depth":3885,"text":3395},[3891,3893,3895,3898,3901,3904,3907,3910,3913],{"lhs":3892,"rhs":2064},"100 * 0.5",{"lhs":3894,"rhs":974},"sqrt(100 * 0.5 * 0.5)",{"lhs":3896,"rhs":3897},"(55 + 0.5 - 50) \u002F 5","1.1",{"lhs":3899,"rhs":3900},"round(0.5 * (1 + erf(1.1 \u002F sqrt(2))), 4)","0.8643",{"lhs":3902,"rhs":3903},"round(sum(map(0:55, f(k) = combinations(100, k) * 0.5^100)), 4)","0.8644",{"lhs":3905,"rhs":3906},"round(0.5 * (1 + erf(1 \u002F sqrt(2))), 4)","0.8413",{"lhs":3908,"rhs":3909},"round(1 \u002F (5 * sqrt(2 * pi)), 4)","0.0798",{"lhs":3911,"rhs":3912},"round(combinations(100, 50) * 0.5^100, 4)","0.0796",{"lhs":3914,"rhs":3915},"round(sqrt(20 * 0.5 * 0.5), 2)","2.24","X \\text{ binomialverteilt mit } n \\text{ und } p,\\ \\sigma > 3","\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 class=\"katex\">binomialverteilt mit\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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\">p\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>σ\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sigma > 3\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\" 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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","moivre-laplace","P(X \\leq k) \\approx \\Phi\\left(\\frac{k + 0{,}5 - \\mu}{\\sigma}\\right), \\quad \\mu = np,\\ \\sigma = \\sqrt{np(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>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>≈\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>0,5\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>σ\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>μ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>σ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\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\">P(X \\leq k) \\approx \\Phi\\left(\\frac{k + 0{,}5 - \\mu}{\\sigma}\\right), \\quad \\mu = np,\\ \\sigma = \\sqrt{np(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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Φ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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\">0\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">5\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\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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\">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\" 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