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",[574,1121,1123,1136],{"className":1122},[577],[574,1124,1126],{"className":1125},[581],[583,1127,1128],{"xmlns":585},[587,1129,1130,1134],{},[590,1131,1132],{},[593,1133,603],{},[626,1135,603],{"encoding":628},[574,1137,1139],{"className":1138,"ariaHidden":634},[633],[574,1140,1142,1145],{"className":1141},[638],[574,1143],{"className":1144,"style":917},[642],[574,1146,603],{"className":1147,"style":657},[647,648],[889,1149,1150],{},[574,1151,1153,1185],{"className":1152},[577],[574,1154,1156],{"className":1155},[581],[583,1157,1158],{"xmlns":585},[587,1159,1160,1182],{},[590,1161,1162,1164,1166,1168,1170,1172,1174,1176,1178,1180],{},[725,1163,733],{},[597,1165,1047],{},[593,1167,612],{},[597,1169,600],{"stretchy":599},[593,1171,617],{},[597,1173,620],{},[593,1175,603],{},[597,1177,1047],{},[725,1179,733],{},[597,1181,606],{"stretchy":599},[626,1183,1184],{"encoding":628},"1 - P(X \\leq k-1)",[574,1186,1188,1207,1231,1249],{"className":1187,"ariaHidden":634},[633],[574,1189,1191,1195,1198,1201,1204],{"className":1190},[638],[574,1192],{"className":1193,"style":1194},[642],"height:0.7278em;vertical-align:-0.0833em;",[574,1196,733],{"className":1197},[647],[574,1199],{"className":1200,"style":1095},[665],[574,1202,1047],{"className":1203},[1099],[574,1205],{"className":1206,"style":1095},[665],[574,1208,1210,1213,1216,1219,1222,1225,1228],{"className":1209},[638],[574,1211],{"className":1212,"style":643},[642],[574,1214,612],{"className":1215,"style":649},[647,648],[574,1217,600],{"className":1218},[653],[574,1220,617],{"className":1221,"style":689},[647,648],[574,1223],{"className":1224,"style":666},[665],[574,1226,620],{"className":1227},[670],[574,1229],{"className":1230,"style":666},[665],[574,1232,1234,1237,1240,1243,1246],{"className":1233},[638],[574,1235],{"className":1236,"style":1088},[642],[574,1238,603],{"className":1239,"style":657},[647,648],[574,1241],{"className":1242,"style":1095},[665],[574,1244,1047],{"className":1245},[1099],[574,1247],{"className":1248,"style":1095},[665],[574,1250,1252,1255,1258],{"className":1251},[638],[574,1253],{"className":1254,"style":643},[642],[574,1256,733],{"className":1257},[647],[574,1259,606],{"className":1260},[661],[874,1262,1263,1294],{},[889,1264,1265,1266],{},"mehr als ",[574,1267,1269,1282],{"className":1268},[577],[574,1270,1272],{"className":1271},[581],[583,1273,1274],{"xmlns":585},[587,1275,1276,1280],{},[590,1277,1278],{},[593,1279,603],{},[626,1281,603],{"encoding":628},[574,1283,1285],{"className":1284,"ariaHidden":634},[633],[574,1286,1288,1291],{"className":1287},[638],[574,1289],{"className":1290,"style":917},[642],[574,1292,603],{"className":1293,"style":657},[647,648],[889,1295,1296],{},[574,1297,1299,1327],{"className":1298},[577],[574,1300,1302],{"className":1301},[581],[583,1303,1304],{"xmlns":585},[587,1305,1306,1324],{},[590,1307,1308,1310,1312,1314,1316,1318,1320,1322],{},[725,1309,733],{},[597,1311,1047],{},[593,1313,612],{},[597,1315,600],{"stretchy":599},[593,1317,617],{},[597,1319,620],{},[593,1321,603],{},[597,1323,606],{"stretchy":599},[626,1325,1326],{"encoding":628},"1 - P(X \\leq k)",[574,1328,1330,1348,1372],{"className":1329,"ariaHidden":634},[633],[574,1331,1333,1336,1339,1342,1345],{"className":1332},[638],[574,1334],{"className":1335,"style":1194},[642],[574,1337,733],{"className":1338},[647],[574,1340],{"className":1341,"style":1095},[665],[574,1343,1047],{"className":1344},[1099],[574,1346],{"className":1347,"style":1095},[665],[574,1349,1351,1354,1357,1360,1363,1366,1369],{"className":1350},[638],[574,1352],{"className":1353,"style":643},[642],[574,1355,612],{"className":1356,"style":649},[647,648],[574,1358,600],{"className":1359},[653],[574,1361,617],{"className":1362,"style":689},[647,648],[574,1364],{"className":1365,"style":666},[665],[574,1367,620],{"className":1368},[670],[574,1370],{"className":1371,"style":666},[665],[574,1373,1375,1378,1381],{"className":1374},[638],[574,1376],{"className":1377,"style":643},[642],[574,1379,603],{"className":1380,"style":657},[647,648],[574,1382,606],{"className":1383},[661],[874,1385,1386,1449],{},[889,1387,1388,1389,1419,1420],{},"zwischen ",[574,1390,1392,1406],{"className":1391},[577],[574,1393,1395],{"className":1394},[581],[583,1396,1397],{"xmlns":585},[587,1398,1399,1404],{},[590,1400,1401],{},[593,1402,1403],{},"a",[626,1405,1403],{"encoding":628},[574,1407,1409],{"className":1408,"ariaHidden":634},[633],[574,1410,1412,1416],{"className":1411},[638],[574,1413],{"className":1414,"style":1415},[642],"height:0.4306em;",[574,1417,1403],{"className":1418},[647,648]," und ",[574,1421,1423,1437],{"className":1422},[577],[574,1424,1426],{"className":1425},[581],[583,1427,1428],{"xmlns":585},[587,1429,1430,1435],{},[590,1431,1432],{},[593,1433,1434],{},"b",[626,1436,1434],{"encoding":628},[574,1438,1440],{"className":1439,"ariaHidden":634},[633],[574,1441,1443,1446],{"className":1442},[638],[574,1444],{"className":1445,"style":917},[642],[574,1447,1434],{"className":1448},[647,648],[889,1450,1451],{},[574,1452,1454,1496],{"className":1453},[577],[574,1455,1457],{"className":1456},[581],[583,1458,1459],{"xmlns":585},[587,1460,1461,1493],{},[590,1462,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491],{},[593,1464,612],{},[597,1466,600],{"stretchy":599},[593,1468,617],{},[597,1470,620],{},[593,1472,1434],{},[597,1474,606],{"stretchy":599},[597,1476,1047],{},[593,1478,612],{},[597,1480,600],{"stretchy":599},[593,1482,617],{},[597,1484,620],{},[593,1486,1403],{},[597,1488,1047],{},[725,1490,733],{},[597,1492,606],{"stretchy":599},[626,1494,1495],{"encoding":628},"P(X \\leq b) - P(X \\leq a-1)",[574,1497,1499,1523,1544,1568,1587],{"className":1498,"ariaHidden":634},[633],[574,1500,1502,1505,1508,1511,1514,1517,1520],{"className":1501},[638],[574,1503],{"className":1504,"style":643},[642],[574,1506,612],{"className":1507,"style":649},[647,648],[574,1509,600],{"className":1510},[653],[574,1512,617],{"className":1513,"style":689},[647,648],[574,1515],{"className":1516,"style":666},[665],[574,1518,620],{"className":1519},[670],[574,1521],{"className":1522,"style":666},[665],[574,1524,1526,1529,1532,1535,1538,1541],{"className":1525},[638],[574,1527],{"className":1528,"style":643},[642],[574,1530,1434],{"className":1531},[647,648],[574,1533,606],{"className":1534},[661],[574,1536],{"className":1537,"style":1095},[665],[574,1539,1047],{"className":1540},[1099],[574,1542],{"className":1543,"style":1095},[665],[574,1545,1547,1550,1553,1556,1559,1562,1565],{"className":1546},[638],[574,1548],{"className":1549,"style":643},[642],[574,1551,612],{"className":1552,"style":649},[647,648],[574,1554,600],{"className":1555},[653],[574,1557,617],{"className":1558,"style":689},[647,648],[574,1560],{"className":1561,"style":666},[665],[574,1563,620],{"className":1564},[670],[574,1566],{"className":1567,"style":666},[665],[574,1569,1571,1575,1578,1581,1584],{"className":1570},[638],[574,1572],{"className":1573,"style":1574},[642],"height:0.6667em;vertical-align:-0.0833em;",[574,1576,1403],{"className":1577},[647,648],[574,1579],{"className":1580,"style":1095},[665],[574,1582,1047],{"className":1583},[1099],[574,1585],{"className":1586,"style":1095},[665],[574,1588,1590,1593,1596],{"className":1589},[638],[574,1591],{"className":1592,"style":643},[642],[574,1594,733],{"className":1595},[647],[574,1597,606],{"className":1598},[661],[565,1600,1601,1602,1631],{},"„Zwischen“ ist dabei einschließlich der Grenzen gemeint. Voraussetzung ist wie bei der Binomialverteilung eine Bernoulli-Kette mit festem ",[574,1603,1605,1618],{"className":1604},[577],[574,1606,1608],{"className":1607},[581],[583,1609,1610],{"xmlns":585},[587,1611,1612,1616],{},[590,1613,1614],{},[593,1615,565],{},[626,1617,565],{"encoding":628},[574,1619,1621],{"className":1620,"ariaHidden":634},[633],[574,1622,1624,1628],{"className":1623},[638],[574,1625],{"className":1626,"style":1627},[642],"height:0.625em;vertical-align:-0.1944em;",[574,1629,565],{"className":1630},[647,648],".",[560,1633,1635],{"id":1634},"beispiele","Beispiele",[565,1637,1638,1667,1668,1419,1722,1785,1786,1814,1815,1631],{},[574,1639,1641,1654],{"className":1640},[577],[574,1642,1644],{"className":1643},[581],[583,1645,1646],{"xmlns":585},[587,1647,1648,1652],{},[590,1649,1650],{},[593,1651,617],{},[626,1653,617],{"encoding":628},[574,1655,1657],{"className":1656,"ariaHidden":634},[633],[574,1658,1660,1664],{"className":1659},[638],[574,1661],{"className":1662,"style":1663},[642],"height:0.6833em;",[574,1665,617],{"className":1666,"style":689},[647,648]," sei binomialverteilt mit ",[574,1669,1671,1691],{"className":1670},[577],[574,1672,1674],{"className":1673},[581],[583,1675,1676],{"xmlns":585},[587,1677,1678,1688],{},[590,1679,1680,1683,1685],{},[593,1681,1682],{},"n",[597,1684,609],{},[725,1686,1687],{},"20",[626,1689,1690],{"encoding":628},"n = 20",[574,1692,1694,1712],{"className":1693,"ariaHidden":634},[633],[574,1695,1697,1700,1703,1706,1709],{"className":1696},[638],[574,1698],{"className":1699,"style":1415},[642],[574,1701,1682],{"className":1702},[647,648],[574,1704],{"className":1705,"style":666},[665],[574,1707,609],{"className":1708},[670],[574,1710],{"className":1711,"style":666},[665],[574,1713,1715,1719],{"className":1714},[638],[574,1716],{"className":1717,"style":1718},[642],"height:0.6444em;",[574,1720,1687],{"className":1721},[647],[574,1723,1725,1744],{"className":1724},[577],[574,1726,1728],{"className":1727},[581],[583,1729,1730],{"xmlns":585},[587,1731,1732,1741],{},[590,1733,1734,1736,1738],{},[593,1735,565],{},[597,1737,609],{},[725,1739,1740],{},"0,3",[626,1742,1743],{"encoding":628},"p = 0{,}3",[574,1745,1747,1765],{"className":1746,"ariaHidden":634},[633],[574,1748,1750,1753,1756,1759,1762],{"className":1749},[638],[574,1751],{"className":1752,"style":1627},[642],[574,1754,565],{"className":1755},[647,648],[574,1757],{"className":1758,"style":666},[665],[574,1760,609],{"className":1761},[670],[574,1763],{"className":1764,"style":666},[665],[574,1766,1768,1772,1775,1781],{"className":1767},[638],[574,1769],{"className":1770,"style":1771},[642],"height:0.8389em;vertical-align:-0.1944em;",[574,1773,727],{"className":1774},[647],[574,1776,1778],{"className":1777},[647],[574,1779,730],{"className":1780},[762],[574,1782,1784],{"className":1783},[647],"3",", z.B. die Anzahl der Treffer bei ",[574,1787,1789,1802],{"className":1788},[577],[574,1790,1792],{"className":1791},[581],[583,1793,1794],{"xmlns":585},[587,1795,1796,1800],{},[590,1797,1798],{},[725,1799,1687],{},[626,1801,1687],{"encoding":628},[574,1803,1805],{"className":1804,"ariaHidden":634},[633],[574,1806,1808,1811],{"className":1807},[638],[574,1809],{"className":1810,"style":1718},[642],[574,1812,1687],{"className":1813},[647]," Würfen mit Trefferquote ",[574,1816,1818,1841],{"className":1817},[577],[574,1819,1821],{"className":1820},[581],[583,1822,1823],{"xmlns":585},[587,1824,1825,1838],{},[590,1826,1827,1830,1834],{},[725,1828,1829],{},"30",[1831,1832,1833],"mtext",{}," ",[593,1835,1837],{"mathvariant":1836},"normal","%",[626,1839,1840],{"encoding":628},"30\\,\\%",[574,1842,1844],{"className":1843,"ariaHidden":634},[633],[574,1845,1847,1851,1854,1857],{"className":1846},[638],[574,1848],{"className":1849,"style":1850},[642],"height:0.8056em;vertical-align:-0.0556em;",[574,1852,1829],{"className":1853},[647],[574,1855],{"className":1856,"style":766},[665],[574,1858,1837],{"className":1859},[647],[565,1861,1862,1863,1892],{},"Höchstens ",[574,1864,1866,1880],{"className":1865},[577],[574,1867,1869],{"className":1868},[581],[583,1870,1871],{"xmlns":585},[587,1872,1873,1878],{},[590,1874,1875],{},[725,1876,1877],{},"4",[626,1879,1877],{"encoding":628},[574,1881,1883],{"className":1882,"ariaHidden":634},[633],[574,1884,1886,1889],{"className":1885},[638],[574,1887],{"className":1888,"style":1718},[642],[574,1890,1877],{"className":1891},[647]," Treffer:",[574,1894,1897],{"className":1895},[1896],"katex-display",[574,1898,1900,1931],{"className":1899},[577],[574,1901,1903],{"className":1902},[581],[583,1904,1906],{"xmlns":585,"display":1905},"block",[587,1907,1908,1928],{},[590,1909,1910,1912,1914,1916,1918,1920,1922,1925],{},[593,1911,612],{},[597,1913,600],{"stretchy":599},[593,1915,617],{},[597,1917,620],{},[725,1919,1877],{},[597,1921,606],{"stretchy":599},[597,1923,1924],{},"≈",[725,1926,1927],{},"0,2375",[626,1929,1930],{"encoding":628},"P(X \\leq 4) \\approx 0{,}2375",[574,1932,1934,1958,1979],{"className":1933,"ariaHidden":634},[633],[574,1935,1937,1940,1943,1946,1949,1952,1955],{"className":1936},[638],[574,1938],{"className":1939,"style":643},[642],[574,1941,612],{"className":1942,"style":649},[647,648],[574,1944,600],{"className":1945},[653],[574,1947,617],{"className":1948,"style":689},[647,648],[574,1950],{"className":1951,"style":666},[665],[574,1953,620],{"className":1954},[670],[574,1956],{"className":1957,"style":666},[665],[574,1959,1961,1964,1967,1970,1973,1976],{"className":1960},[638],[574,1962],{"className":1963,"style":643},[642],[574,1965,1877],{"className":1966},[647],[574,1968,606],{"className":1969},[661],[574,1971],{"className":1972,"style":666},[665],[574,1974,1924],{"className":1975},[670],[574,1977],{"className":1978,"style":666},[665],[574,1980,1982,1985,1988,1994],{"className":1981},[638],[574,1983],{"className":1984,"style":1771},[642],[574,1986,727],{"className":1987},[647],[574,1989,1991],{"className":1990},[647],[574,1992,730],{"className":1993},[762],[574,1995,1997],{"className":1996},[647],"2375",[565,1999,2000,2001,1892],{},"Mindestens ",[574,2002,2004,2018],{"className":2003},[577],[574,2005,2007],{"className":2006},[581],[583,2008,2009],{"xmlns":585},[587,2010,2011,2016],{},[590,2012,2013],{},[725,2014,2015],{},"8",[626,2017,2015],{"encoding":628},[574,2019,2021],{"className":2020,"ariaHidden":634},[633],[574,2022,2024,2027],{"className":2023},[638],[574,2025],{"className":2026,"style":1718},[642],[574,2028,2015],{"className":2029},[647],[574,2031,2033],{"className":2032},[1896],[574,2034,2036,2094],{"className":2035},[577],[574,2037,2039],{"className":2038},[581],[583,2040,2041],{"xmlns":585,"display":1905},[587,2042,2043,2091],{},[590,2044,2045,2047,2049,2051,2054,2056,2058,2060,2062,2064,2066,2068,2070,2072,2075,2077,2079,2081,2083,2086,2088],{},[593,2046,612],{},[597,2048,600],{"stretchy":599},[593,2050,617],{},[597,2052,2053],{},"≥",[725,2055,2015],{},[597,2057,606],{"stretchy":599},[597,2059,609],{},[725,2061,733],{},[597,2063,1047],{},[593,2065,612],{},[597,2067,600],{"stretchy":599},[593,2069,617],{},[597,2071,620],{},[725,2073,2074],{},"7",[597,2076,606],{"stretchy":599},[597,2078,1924],{},[725,2080,733],{},[597,2082,1047],{},[725,2084,2085],{},"0,7723",[597,2087,609],{},[725,2089,2090],{},"0,2277",[626,2092,2093],{"encoding":628},"P(X \\geq 8) = 1 - P(X \\leq 7) \\approx 1 - 0{,}7723 = 0{,}2277",[574,2095,2097,2121,2142,2160,2184,2205,2223,2251],{"className":2096,"ariaHidden":634},[633],[574,2098,2100,2103,2106,2109,2112,2115,2118],{"className":2099},[638],[574,2101],{"className":2102,"style":643},[642],[574,2104,612],{"className":2105,"style":649},[647,648],[574,2107,600],{"className":2108},[653],[574,2110,617],{"className":2111,"style":689},[647,648],[574,2113],{"className":2114,"style":666},[665],[574,2116,2053],{"className":2117},[670],[574,2119],{"className":2120,"style":666},[665],[574,2122,2124,2127,2130,2133,2136,2139],{"className":2123},[638],[574,2125],{"className":2126,"style":643},[642],[574,2128,2015],{"className":2129},[647],[574,2131,606],{"className":2132},[661],[574,2134],{"className":2135,"style":666},[665],[574,2137,609],{"className":2138},[670],[574,2140],{"className":2141,"style":666},[665],[574,2143,2145,2148,2151,2154,2157],{"className":2144},[638],[574,2146],{"className":2147,"style":1194},[642],[574,2149,733],{"className":2150},[647],[574,2152],{"className":2153,"style":1095},[665],[574,2155,1047],{"className":2156},[1099],[574,2158],{"className":2159,"style":1095},[665],[574,2161,2163,2166,2169,2172,2175,2178,2181],{"className":2162},[638],[574,2164],{"className":2165,"style":643},[642],[574,2167,612],{"className":2168,"style":649},[647,648],[574,2170,600],{"className":2171},[653],[574,2173,617],{"className":2174,"style":689},[647,648],[574,2176],{"className":2177,"style":666},[665],[574,2179,620],{"className":2180},[670],[574,2182],{"className":2183,"style":666},[665],[574,2185,2187,2190,2193,2196,2199,2202],{"className":2186},[638],[574,2188],{"className":2189,"style":643},[642],[574,2191,2074],{"className":2192},[647],[574,2194,606],{"className":2195},[661],[574,2197],{"className":2198,"style":666},[665],[574,2200,1924],{"className":2201},[670],[574,2203],{"className":2204,"style":666},[665],[574,2206,2208,2211,2214,2217,2220],{"className":2207},[638],[574,2209],{"className":2210,"style":1194},[642],[574,2212,733],{"className":2213},[647],[574,2215],{"className":2216,"style":1095},[665],[574,2218,1047],{"className":2219},[1099],[574,2221],{"className":2222,"style":1095},[665],[574,2224,2226,2229,2232,2238,2242,2245,2248],{"className":2225},[638],[574,2227],{"className":2228,"style":1771},[642],[574,2230,727],{"className":2231},[647],[574,2233,2235],{"className":2234},[647],[574,2236,730],{"className":2237},[762],[574,2239,2241],{"className":2240},[647],"7723",[574,2243],{"className":2244,"style":666},[665],[574,2246,609],{"className":2247},[670],[574,2249],{"className":2250,"style":666},[665],[574,2252,2254,2257,2260,2266],{"className":2253},[638],[574,2255],{"className":2256,"style":1771},[642],[574,2258,727],{"className":2259},[647],[574,2261,2263],{"className":2262},[647],[574,2264,730],{"className":2265},[762],[574,2267,2269],{"className":2268},[647],"2277",[565,2271,2272,2273,1419,2301,2329],{},"Zwischen ",[574,2274,2276,2289],{"className":2275},[577],[574,2277,2279],{"className":2278},[581],[583,2280,2281],{"xmlns":585},[587,2282,2283,2287],{},[590,2284,2285],{},[725,2286,1784],{},[626,2288,1784],{"encoding":628},[574,2290,2292],{"className":2291,"ariaHidden":634},[633],[574,2293,2295,2298],{"className":2294},[638],[574,2296],{"className":2297,"style":1718},[642],[574,2299,1784],{"className":2300},[647],[574,2302,2304,2317],{"className":2303},[577],[574,2305,2307],{"className":2306},[581],[583,2308,2309],{"xmlns":585},[587,2310,2311,2315],{},[590,2312,2313],{},[725,2314,2074],{},[626,2316,2074],{"encoding":628},[574,2318,2320],{"className":2319,"ariaHidden":634},[633],[574,2321,2323,2326],{"className":2322},[638],[574,2324],{"className":2325,"style":1718},[642],[574,2327,2074],{"className":2328},[647]," Treffern:",[574,2331,2333],{"className":2332},[1896],[574,2334,2336,2407],{"className":2335},[577],[574,2337,2339],{"className":2338},[581],[583,2340,2341],{"xmlns":585,"display":1905},[587,2342,2343,2404],{},[590,2344,2345,2347,2349,2351,2353,2355,2357,2359,2361,2363,2365,2367,2369,2371,2373,2375,2377,2379,2381,2383,2385,2388,2390,2392,2394,2396,2399,2401],{},[593,2346,612],{},[597,2348,600],{"stretchy":599},[725,2350,1784],{},[597,2352,620],{},[593,2354,617],{},[597,2356,620],{},[725,2358,2074],{},[597,2360,606],{"stretchy":599},[597,2362,609],{},[593,2364,612],{},[597,2366,600],{"stretchy":599},[593,2368,617],{},[597,2370,620],{},[725,2372,2074],{},[597,2374,606],{"stretchy":599},[597,2376,1047],{},[593,2378,612],{},[597,2380,600],{"stretchy":599},[593,2382,617],{},[597,2384,620],{},[725,2386,2387],{},"2",[597,2389,606],{"stretchy":599},[597,2391,1924],{},[725,2393,2085],{},[597,2395,1047],{},[725,2397,2398],{},"0,0355",[597,2400,609],{},[725,2402,2403],{},"0,7368",[626,2405,2406],{"encoding":628},"P(3 \\leq X \\leq 7) = P(X \\leq 7) - P(X \\leq 2) \\approx 0{,}7723 - 0{,}0355 = 0{,}7368",[574,2408,2410,2434,2453,2474,2498,2519,2543,2564,2591,2619],{"className":2409,"ariaHidden":634},[633],[574,2411,2413,2416,2419,2422,2425,2428,2431],{"className":2412},[638],[574,2414],{"className":2415,"style":643},[642],[574,2417,612],{"className":2418,"style":649},[647,648],[574,2420,600],{"className":2421},[653],[574,2423,1784],{"className":2424},[647],[574,2426],{"className":2427,"style":666},[665],[574,2429,620],{"className":2430},[670],[574,2432],{"className":2433,"style":666},[665],[574,2435,2437,2441,2444,2447,2450],{"className":2436},[638],[574,2438],{"className":2439,"style":2440},[642],"height:0.8193em;vertical-align:-0.136em;",[574,2442,617],{"className":2443,"style":689},[647,648],[574,2445],{"className":2446,"style":666},[665],[574,2448,620],{"className":2449},[670],[574,2451],{"className":2452,"style":666},[665],[574,2454,2456,2459,2462,2465,2468,2471],{"className":2455},[638],[574,2457],{"className":2458,"style":643},[642],[574,2460,2074],{"className":2461},[647],[574,2463,606],{"className":2464},[661],[574,2466],{"className":2467,"style":666},[665],[574,2469,609],{"className":2470},[670],[574,2472],{"className":2473,"style":666},[665],[574,2475,2477,2480,2483,2486,2489,2492,2495],{"className":2476},[638],[574,2478],{"className":2479,"style":643},[642],[574,2481,612],{"className":2482,"style":649},[647,648],[574,2484,600],{"className":2485},[653],[574,2487,617],{"className":2488,"style":689},[647,648],[574,2490],{"className":2491,"style":666},[665],[574,2493,620],{"className":2494},[670],[574,2496],{"className":2497,"style":666},[665],[574,2499,2501,2504,2507,2510,2513,2516],{"className":2500},[638],[574,2502],{"className":2503,"style":643},[642],[574,2505,2074],{"className":2506},[647],[574,2508,606],{"className":2509},[661],[574,2511],{"className":2512,"style":1095},[665],[574,2514,1047],{"className":2515},[1099],[574,2517],{"className":2518,"style":1095},[665],[574,2520,2522,2525,2528,2531,2534,2537,2540],{"className":2521},[638],[574,2523],{"className":2524,"style":643},[642],[574,2526,612],{"className":2527,"style":649},[647,648],[574,2529,600],{"className":2530},[653],[574,2532,617],{"className":2533,"style":689},[647,648],[574,2535],{"className":2536,"style":666},[665],[574,2538,620],{"className":2539},[670],[574,2541],{"className":2542,"style":666},[665],[574,2544,2546,2549,2552,2555,2558,2561],{"className":2545},[638],[574,2547],{"className":2548,"style":643},[642],[574,2550,2387],{"className":2551},[647],[574,2553,606],{"className":2554},[661],[574,2556],{"className":2557,"style":666},[665],[574,2559,1924],{"className":2560},[670],[574,2562],{"className":2563,"style":666},[665],[574,2565,2567,2570,2573,2579,2582,2585,2588],{"className":2566},[638],[574,2568],{"className":2569,"style":1771},[642],[574,2571,727],{"className":2572},[647],[574,2574,2576],{"className":2575},[647],[574,2577,730],{"className":2578},[762],[574,2580,2241],{"className":2581},[647],[574,2583],{"className":2584,"style":1095},[665],[574,2586,1047],{"className":2587},[1099],[574,2589],{"className":2590,"style":1095},[665],[574,2592,2594,2597,2600,2606,2610,2613,2616],{"className":2593},[638],[574,2595],{"className":2596,"style":1771},[642],[574,2598,727],{"className":2599},[647],[574,2601,2603],{"className":2602},[647],[574,2604,730],{"className":2605},[762],[574,2607,2609],{"className":2608},[647],"0355",[574,2611],{"className":2612,"style":666},[665],[574,2614,609],{"className":2615},[670],[574,2617],{"className":2618,"style":666},[665],[574,2620,2622,2625,2628,2634],{"className":2621},[638],[574,2623],{"className":2624,"style":1771},[642],[574,2626,727],{"className":2627},[647],[574,2629,2631],{"className":2630},[647],[574,2632,730],{"className":2633},[762],[574,2635,2637],{"className":2636},[647],"7368",[560,2639,2641],{"id":2640},"typische-fehler","Typische Fehler",[2643,2644,2645,2940,3185,3315],"ul",{},[2646,2647,2648,2649,2677,2678,2799,2800,2851,2852,1631],"li",{},"Bei „mindestens ",[574,2650,2652,2665],{"className":2651},[577],[574,2653,2655],{"className":2654},[581],[583,2656,2657],{"xmlns":585},[587,2658,2659,2663],{},[590,2660,2661],{},[725,2662,2015],{},[626,2664,2015],{"encoding":628},[574,2666,2668],{"className":2667,"ariaHidden":634},[633],[574,2669,2671,2674],{"className":2670},[638],[574,2672],{"className":2673,"style":1718},[642],[574,2675,2015],{"className":2676},[647],"“ mit ",[574,2679,2681,2714],{"className":2680},[577],[574,2682,2684],{"className":2683},[581],[583,2685,2686],{"xmlns":585},[587,2687,2688,2711],{},[590,2689,2690,2692,2694,2696,2698,2700,2702,2704,2706,2708],{},[725,2691,733],{},[597,2693,1047],{},[593,2695,612],{},[597,2697,600],{"stretchy":599},[593,2699,617],{},[597,2701,620],{},[725,2703,2015],{},[597,2705,606],{"stretchy":599},[597,2707,1924],{},[725,2709,2710],{},"0,1133",[626,2712,2713],{"encoding":628},"1 - P(X \\leq 8) \\approx 0{,}1133",[574,2715,2717,2735,2759,2780],{"className":2716,"ariaHidden":634},[633],[574,2718,2720,2723,2726,2729,2732],{"className":2719},[638],[574,2721],{"className":2722,"style":1194},[642],[574,2724,733],{"className":2725},[647],[574,2727],{"className":2728,"style":1095},[665],[574,2730,1047],{"className":2731},[1099],[574,2733],{"className":2734,"style":1095},[665],[574,2736,2738,2741,2744,2747,2750,2753,2756],{"className":2737},[638],[574,2739],{"className":2740,"style":643},[642],[574,2742,612],{"className":2743,"style":649},[647,648],[574,2745,600],{"className":2746},[653],[574,2748,617],{"className":2749,"style":689},[647,648],[574,2751],{"className":2752,"style":666},[665],[574,2754,620],{"className":2755},[670],[574,2757],{"className":2758,"style":666},[665],[574,2760,2762,2765,2768,2771,2774,2777],{"className":2761},[638],[574,2763],{"className":2764,"style":643},[642],[574,2766,2015],{"className":2767},[647],[574,2769,606],{"className":2770},[661],[574,2772],{"className":2773,"style":666},[665],[574,2775,1924],{"className":2776},[670],[574,2778],{"className":2779,"style":666},[665],[574,2781,2783,2786,2789,2795],{"className":2782},[638],[574,2784],{"className":2785,"style":1771},[642],[574,2787,727],{"className":2788},[647],[574,2790,2792],{"className":2791},[647],[574,2793,730],{"className":2794},[762],[574,2796,2798],{"className":2797},[647],"1133"," rechnen. Damit fehlt der Wert ",[574,2801,2803,2821],{"className":2802},[577],[574,2804,2806],{"className":2805},[581],[583,2807,2808],{"xmlns":585},[587,2809,2810,2818],{},[590,2811,2812,2814,2816],{},[593,2813,617],{},[597,2815,609],{},[725,2817,2015],{},[626,2819,2820],{"encoding":628},"X = 8",[574,2822,2824,2842],{"className":2823,"ariaHidden":634},[633],[574,2825,2827,2830,2833,2836,2839],{"className":2826},[638],[574,2828],{"className":2829,"style":1663},[642],[574,2831,617],{"className":2832,"style":689},[647,648],[574,2834],{"className":2835,"style":666},[665],[574,2837,609],{"className":2838},[670],[574,2840],{"className":2841,"style":666},[665],[574,2843,2845,2848],{"className":2844},[638],[574,2846],{"className":2847,"style":1718},[642],[574,2849,2015],{"className":2850},[647],"; richtig ist ",[574,2853,2855,2883],{"className":2854},[577],[574,2856,2858],{"className":2857},[581],[583,2859,2860],{"xmlns":585},[587,2861,2862,2880],{},[590,2863,2864,2866,2868,2870,2872,2874,2876,2878],{},[725,2865,733],{},[597,2867,1047],{},[593,2869,612],{},[597,2871,600],{"stretchy":599},[593,2873,617],{},[597,2875,620],{},[725,2877,2074],{},[597,2879,606],{"stretchy":599},[626,2881,2882],{"encoding":628},"1 - P(X \\leq 7)",[574,2884,2886,2904,2928],{"className":2885,"ariaHidden":634},[633],[574,2887,2889,2892,2895,2898,2901],{"className":2888},[638],[574,2890],{"className":2891,"style":1194},[642],[574,2893,733],{"className":2894},[647],[574,2896],{"className":2897,"style":1095},[665],[574,2899,1047],{"className":2900},[1099],[574,2902],{"className":2903,"style":1095},[665],[574,2905,2907,2910,2913,2916,2919,2922,2925],{"className":2906},[638],[574,2908],{"className":2909,"style":643},[642],[574,2911,612],{"className":2912,"style":649},[647,648],[574,2914,600],{"className":2915},[653],[574,2917,617],{"className":2918,"style":689},[647,648],[574,2920],{"className":2921,"style":666},[665],[574,2923,620],{"className":2924},[670],[574,2926],{"className":2927,"style":666},[665],[574,2929,2931,2934,2937],{"className":2930},[638],[574,2932],{"className":2933,"style":643},[642],[574,2935,2074],{"className":2936},[647],[574,2938,606],{"className":2939},[661],[2646,2941,2942,2943,1419,2971,2999,3000,3066,3067,3118,3119,1631],{},"Bei „zwischen ",[574,2944,2946,2959],{"className":2945},[577],[574,2947,2949],{"className":2948},[581],[583,2950,2951],{"xmlns":585},[587,2952,2953,2957],{},[590,2954,2955],{},[725,2956,1784],{},[626,2958,1784],{"encoding":628},[574,2960,2962],{"className":2961,"ariaHidden":634},[633],[574,2963,2965,2968],{"className":2964},[638],[574,2966],{"className":2967,"style":1718},[642],[574,2969,1784],{"className":2970},[647],[574,2972,2974,2987],{"className":2973},[577],[574,2975,2977],{"className":2976},[581],[583,2978,2979],{"xmlns":585},[587,2980,2981,2985],{},[590,2982,2983],{},[725,2984,2074],{},[626,2986,2074],{"encoding":628},[574,2988,2990],{"className":2989,"ariaHidden":634},[633],[574,2991,2993,2996],{"className":2992},[638],[574,2994],{"className":2995,"style":1718},[642],[574,2997,2074],{"className":2998},[647],"“ ",[574,3001,3003,3027],{"className":3002},[577],[574,3004,3006],{"className":3005},[581],[583,3007,3008],{"xmlns":585},[587,3009,3010,3024],{},[590,3011,3012,3014,3016,3018,3020,3022],{},[593,3013,612],{},[597,3015,600],{"stretchy":599},[593,3017,617],{},[597,3019,620],{},[725,3021,1784],{},[597,3023,606],{"stretchy":599},[626,3025,3026],{"encoding":628},"P(X \\leq 3)",[574,3028,3030,3054],{"className":3029,"ariaHidden":634},[633],[574,3031,3033,3036,3039,3042,3045,3048,3051],{"className":3032},[638],[574,3034],{"className":3035,"style":643},[642],[574,3037,612],{"className":3038,"style":649},[647,648],[574,3040,600],{"className":3041},[653],[574,3043,617],{"className":3044,"style":689},[647,648],[574,3046],{"className":3047,"style":666},[665],[574,3049,620],{"className":3050},[670],[574,3052],{"className":3053,"style":666},[665],[574,3055,3057,3060,3063],{"className":3056},[638],[574,3058],{"className":3059,"style":643},[642],[574,3061,1784],{"className":3062},[647],[574,3064,606],{"className":3065},[661]," abziehen. Dann fehlt ",[574,3068,3070,3088],{"className":3069},[577],[574,3071,3073],{"className":3072},[581],[583,3074,3075],{"xmlns":585},[587,3076,3077,3085],{},[590,3078,3079,3081,3083],{},[593,3080,617],{},[597,3082,609],{},[725,3084,1784],{},[626,3086,3087],{"encoding":628},"X = 3",[574,3089,3091,3109],{"className":3090,"ariaHidden":634},[633],[574,3092,3094,3097,3100,3103,3106],{"className":3093},[638],[574,3095],{"className":3096,"style":1663},[642],[574,3098,617],{"className":3099,"style":689},[647,648],[574,3101],{"className":3102,"style":666},[665],[574,3104,609],{"className":3105},[670],[574,3107],{"className":3108,"style":666},[665],[574,3110,3112,3115],{"className":3111},[638],[574,3113],{"className":3114,"style":1718},[642],[574,3116,1784],{"className":3117},[647],"; abgezogen wird ",[574,3120,3122,3146],{"className":3121},[577],[574,3123,3125],{"className":3124},[581],[583,3126,3127],{"xmlns":585},[587,3128,3129,3143],{},[590,3130,3131,3133,3135,3137,3139,3141],{},[593,3132,612],{},[597,3134,600],{"stretchy":599},[593,3136,617],{},[597,3138,620],{},[725,3140,2387],{},[597,3142,606],{"stretchy":599},[626,3144,3145],{"encoding":628},"P(X \\leq 2)",[574,3147,3149,3173],{"className":3148,"ariaHidden":634},[633],[574,3150,3152,3155,3158,3161,3164,3167,3170],{"className":3151},[638],[574,3153],{"className":3154,"style":643},[642],[574,3156,612],{"className":3157,"style":649},[647,648],[574,3159,600],{"className":3160},[653],[574,3162,617],{"className":3163,"style":689},[647,648],[574,3165],{"className":3166,"style":666},[665],[574,3168,620],{"className":3169},[670],[574,3171],{"className":3172,"style":666},[665],[574,3174,3176,3179,3182],{"className":3175},[638],[574,3177],{"className":3178,"style":643},[642],[574,3180,2387],{"className":3181},[647],[574,3183,606],{"className":3184},[661],[2646,3186,3187,3188,1631],{},"„Weniger als“ und „höchstens“ gleich behandeln. ",[574,3189,3191,3231],{"className":3190},[577],[574,3192,3194],{"className":3193},[581],[583,3195,3196],{"xmlns":585},[587,3197,3198,3228],{},[590,3199,3200,3202,3204,3206,3209,3212,3214,3216,3218,3220,3222,3224,3226],{},[593,3201,612],{},[597,3203,600],{"stretchy":599},[593,3205,617],{},[597,3207,3208],{},"\u003C",[725,3210,3211],{},"5",[597,3213,606],{"stretchy":599},[597,3215,609],{},[593,3217,612],{},[597,3219,600],{"stretchy":599},[593,3221,617],{},[597,3223,620],{},[725,3225,1877],{},[597,3227,606],{"stretchy":599},[626,3229,3230],{"encoding":628},"P(X \u003C 5) = P(X \\leq 4)",[574,3232,3234,3258,3279,3303],{"className":3233,"ariaHidden":634},[633],[574,3235,3237,3240,3243,3246,3249,3252,3255],{"className":3236},[638],[574,3238],{"className":3239,"style":643},[642],[574,3241,612],{"className":3242,"style":649},[647,648],[574,3244,600],{"className":3245},[653],[574,3247,617],{"className":3248,"style":689},[647,648],[574,3250],{"className":3251,"style":666},[665],[574,3253,3208],{"className":3254},[670],[574,3256],{"className":3257,"style":666},[665],[574,3259,3261,3264,3267,3270,3273,3276],{"className":3260},[638],[574,3262],{"className":3263,"style":643},[642],[574,3265,3211],{"className":3266},[647],[574,3268,606],{"className":3269},[661],[574,3271],{"className":3272,"style":666},[665],[574,3274,609],{"className":3275},[670],[574,3277],{"className":3278,"style":666},[665],[574,3280,3282,3285,3288,3291,3294,3297,3300],{"className":3281},[638],[574,3283],{"className":3284,"style":643},[642],[574,3286,612],{"className":3287,"style":649},[647,648],[574,3289,600],{"className":3290},[653],[574,3292,617],{"className":3293,"style":689},[647,648],[574,3295],{"className":3296,"style":666},[665],[574,3298,620],{"className":3299},[670],[574,3301],{"className":3302,"style":666},[665],[574,3304,3306,3309,3312],{"className":3305},[638],[574,3307],{"className":3308,"style":643},[642],[574,3310,1877],{"className":3311},[647],[574,3313,606],{"className":3314},[661],[2646,3316,3317,3318,3384,3385,1631],{},"Kumulierte und einzelne Werte verwechseln: ",[574,3319,3321,3345],{"className":3320},[577],[574,3322,3324],{"className":3323},[581],[583,3325,3326],{"xmlns":585},[587,3327,3328,3342],{},[590,3329,3330,3332,3334,3336,3338,3340],{},[593,3331,612],{},[597,3333,600],{"stretchy":599},[593,3335,617],{},[597,3337,620],{},[725,3339,1877],{},[597,3341,606],{"stretchy":599},[626,3343,3344],{"encoding":628},"P(X \\leq 4)",[574,3346,3348,3372],{"className":3347,"ariaHidden":634},[633],[574,3349,3351,3354,3357,3360,3363,3366,3369],{"className":3350},[638],[574,3352],{"className":3353,"style":643},[642],[574,3355,612],{"className":3356,"style":649},[647,648],[574,3358,600],{"className":3359},[653],[574,3361,617],{"className":3362,"style":689},[647,648],[574,3364],{"className":3365,"style":666},[665],[574,3367,620],{"className":3368},[670],[574,3370],{"className":3371,"style":666},[665],[574,3373,3375,3378,3381],{"className":3374},[638],[574,3376],{"className":3377,"style":643},[642],[574,3379,1877],{"className":3380},[647],[574,3382,606],{"className":3383},[661]," ist nicht ",[574,3386,3388,3412],{"className":3387},[577],[574,3389,3391],{"className":3390},[581],[583,3392,3393],{"xmlns":585},[587,3394,3395,3409],{},[590,3396,3397,3399,3401,3403,3405,3407],{},[593,3398,612],{},[597,3400,600],{"stretchy":599},[593,3402,617],{},[597,3404,609],{},[725,3406,1877],{},[597,3408,606],{"stretchy":599},[626,3410,3411],{"encoding":628},"P(X = 4)",[574,3413,3415,3439],{"className":3414,"ariaHidden":634},[633],[574,3416,3418,3421,3424,3427,3430,3433,3436],{"className":3417},[638],[574,3419],{"className":3420,"style":643},[642],[574,3422,612],{"className":3423,"style":649},[647,648],[574,3425,600],{"className":3426},[653],[574,3428,617],{"className":3429,"style":689},[647,648],[574,3431],{"className":3432,"style":666},[665],[574,3434,609],{"className":3435},[670],[574,3437],{"className":3438,"style":666},[665],[574,3440,3442,3445,3448],{"className":3441},[638],[574,3443],{"className":3444,"style":643},[642],[574,3446,1877],{"className":3447},[647],[574,3449,606],{"className":3450},[661],{"title":3452,"searchDepth":3453,"depth":3453,"links":3454},"",2,[3455,3456,3457],{"id":562,"depth":3453,"text":563},{"id":1634,"depth":3453,"text":1635},{"id":2640,"depth":3453,"text":2641},[3459,3461,3464,3467,3470,3473,3476],{"lhs":3460,"rhs":733},"(1-p)^3 + 3*p*(1-p)^2 + 3*p^2*(1-p) + p^3",{"lhs":3462,"rhs":3463},"round(sum(map(0:4, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.2375",{"lhs":3465,"rhs":3466},"round(sum(map(0:7, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.7723",{"lhs":3468,"rhs":3469},"round(1 - sum(map(0:7, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.2277",{"lhs":3471,"rhs":3472},"round(sum(map(0:2, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.0355",{"lhs":3474,"rhs":3475},"round(sum(map(3:7, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.7368",{"lhs":3477,"rhs":3478},"round(1 - sum(map(0:8, f(j) = combinations(20, j) * 0.3^j * 0.7^(20 - j))), 4)","0.1133","X \\text{ binomialverteilt mit } n \\text{ und } p,\\ k \\in \\{0, 1, \\ldots, n\\}","\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>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmo stretchy=\"false\">{\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">}\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\{0, 1, \\ldots, 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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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=\"mopen\">{\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">}\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","cumulative-binomial","P(X \\leq k) = \\sum_{j=0}^{k} \\binom{n}{j} \\cdot p^j \\cdot (1-p)^{n-j}","\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>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>n\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X \\leq k) = \\sum_{j=0}^{k} \\binom{n}{j} \\cdot p^j \\cdot (1-p)^{n-j}\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:3.2499em;vertical-align:-1.4138em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.8361em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\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:1.4138em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\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:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.2222em;\">\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:1.0691em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8747em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1em;vertical-align:-0.25em;\">\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1247em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8747em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fkumulierte-binomialverteilung",[],[3492,3493,3494,3495],"binomial-distribution","complement-probability","binomial-mean-sd","rejection-region",{"title":548,"description":3452},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fkumulierte-binomialverteilung","Die Wahrscheinlichkeit für höchstens k Treffer ist die Summe der Binomialwahrscheinlichkeiten für 0 bis k Treffer.",[3500,3501,3502,3503,3504],"binomialverteilung","höchstens","mindestens","summenfunktion","bernoulli-kette",[3506,3509,3512,3515,3518],{"symbol":826,"meaning":3507,"symbolHtml":3508},"Wahrscheinlichkeit für höchstens k Treffer","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X \\leq k)\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1682,"meaning":3510,"symbolHtml":3511},"Länge der Bernoulli-Kette","\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>",{"symbol":565,"meaning":3513,"symbolHtml":3514},"Trefferwahrscheinlichkeit bei jedem Versuch","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":603,"meaning":3516,"symbolHtml":3517},"obere Grenze für die Trefferzahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3519,"meaning":3520,"symbolHtml":3521},"j","Laufindex, die einzelnen Trefferzahlen von 0 bis k","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">j\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:0.854em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","oIfKTCKMnCDrflMXhHeC3vXznVCZhUIaWIsjx8I5pRM",[3524,3527,3530,3533],{"stem":3525,"title":3526,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fablehnungsbereich","Ablehnungsbereich bei der Binomialverteilung",{"stem":3528,"title":3529,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":3531,"title":3532,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert-und-standardabweichung-binomialverteilung","Erwartungswert und Standardabweichung der Binomialverteilung",{"stem":3534,"title":3535,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fgegenwahrscheinlichkeit","Gegenwahrscheinlichkeit",1793824286315]