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",[583,1177,1179,1198],{"className":1178},[586],[583,1180,1182],{"className":1181},[590],[592,1183,1184],{"xmlns":594},[596,1185,1186,1195],{},[599,1187,1188,1190,1192],{},[602,1189,942],{},[606,1191,608],{},[610,1193,1194],{},"1",[614,1196,1197],{"encoding":616},"\\sigma = 1",[583,1199,1201,1219],{"className":1200,"ariaHidden":622},[621],[583,1202,1204,1207,1210,1213,1216],{"className":1203},[626],[583,1205],{"className":1206,"style":631},[630],[583,1208,942],{"className":1209,"style":958},[635,636],[583,1211],{"className":1212,"style":642},[641],[583,1214,608],{"className":1215},[646],[583,1217],{"className":1218,"style":642},[641],[583,1220,1222,1225],{"className":1221},[626],[583,1223],{"className":1224,"style":656},[630],[583,1226,1194],{"className":1227},[635],"). Deshalb genügt eine einzige Tabelle der Verteilungsfunktion ",[583,1230,1232,1248],{"className":1231},[586],[583,1233,1235],{"className":1234},[590],[592,1236,1237],{"xmlns":594},[596,1238,1239,1245],{},[599,1240,1241],{},[602,1242,1244],{"mathvariant":1243},"normal","Φ",[614,1246,1247],{"encoding":616},"\\Phi",[583,1249,1251],{"className":1250,"ariaHidden":622},[621],[583,1252,1254,1257],{"className":1253},[626],[583,1255],{"className":1256,"style":893},[630],[583,1258,1244],{"className":1259},[635],":",[583,1262,1265],{"className":1263},[1264],"katex-display",[583,1266,1268,1325],{"className":1267},[586],[583,1269,1271],{"className":1270},[590],[592,1272,1274],{"xmlns":594,"display":1273},"block",[596,1275,1276,1322],{},[599,1277,1278,1281,1285,1287,1290,1293,1296,1298,1300,1304],{},[602,1279,1280],{},"P",[606,1282,1284],{"stretchy":1283},"false","(",[602,1286,881],{},[606,1288,1289],{},"≤",[602,1291,1292],{},"x",[606,1294,1295],{"stretchy":1283},")",[606,1297,608],{},[602,1299,1244],{"mathvariant":1243},[1301,1302,1303],"mtext",{}," ⁣",[599,1305,1306,1308,1320],{},[606,1307,1284],{"fence":622},[978,1309,1310,1318],{},[599,1311,1312,1314,1316],{},[602,1313,1292],{},[606,1315,986],{},[602,1317,675],{},[602,1319,942],{},[606,1321,1295],{"fence":622},[614,1323,1324],{"encoding":616},"P(X \\leq x) = \\Phi\\!\\left(\\frac{x - \\mu}{\\sigma}\\right)",[583,1326,1328,1354,1375],{"className":1327,"ariaHidden":622},[621],[583,1329,1331,1335,1339,1342,1345,1348,1351],{"className":1330},[626],[583,1332],{"className":1333,"style":1334},[630],"height:1em;vertical-align:-0.25em;",[583,1336,1280],{"className":1337,"style":1338},[635,636],"margin-right:0.1389em;",[583,1340,1284],{"className":1341},[1029],[583,1343,881],{"className":1344,"style":897},[635,636],[583,1346],{"className":1347,"style":642},[641],[583,1349,1289],{"className":1350},[646],[583,1352],{"className":1353,"style":642},[641],[583,1355,1357,1360,1363,1366,1369,1372],{"className":1356},[626],[583,1358],{"className":1359,"style":1334},[630],[583,1361,1292],{"className":1362},[635,636],[583,1364,1295],{"className":1365},[1119],[583,1367],{"className":1368,"style":642},[641],[583,1370,608],{"className":1371},[646],[583,1373],{"className":1374,"style":642},[641],[583,1376,1378,1382,1385,1389,1393],{"className":1377},[626],[583,1379],{"className":1380,"style":1381},[630],"height:2.4em;vertical-align:-0.95em;",[583,1383,1244],{"className":1384},[635],[583,1386],{"className":1387,"style":1388},[641],"margin-right:-0.1667em;",[583,1390],{"className":1391,"style":1392},[641],"margin-right:0.1667em;",[583,1394,1397,1406,1485],{"className":1395},[1396],"minner",[583,1398,1402],{"className":1399,"style":1401},[1029,1400],"delimcenter","top:0em;",[583,1403,1284],{"className":1404},[1405,1061],"delimsizing",[583,1407,1409,1412,1482],{"className":1408},[635],[583,1410],{"className":1411},[1029,1030],[583,1413,1415],{"className":1414},[978],[583,1416,1418,1473],{"className":1417},[1037,1038],[583,1419,1421,1470],{"className":1420},[1042],[583,1422,1425,1437,1445],{"className":1423,"style":1424},[1046],"height:1.2603em;",[583,1426,1428,1431],{"style":1427},"top:-2.314em;",[583,1429],{"className":1430,"style":1055},[1054],[583,1432,1434],{"className":1433},[635],[583,1435,942],{"className":1436,"style":958},[635,636],[583,1438,1439,1442],{"style":1071},[583,1440],{"className":1441,"style":1055},[1054],[583,1443],{"className":1444,"style":1079},[1078],[583,1446,1448,1451],{"style":1447},"top:-3.677em;",[583,1449],{"className":1450,"style":1055},[1054],[583,1452,1454,1457,1461,1464,1467],{"className":1453},[635],[583,1455,1292],{"className":1456},[635,636],[583,1458],{"className":1459,"style":1460},[641],"margin-right:0.2222em;",[583,1462,986],{"className":1463},[1098],[583,1465],{"className":1466,"style":1460},[641],[583,1468,675],{"className":1469},[635,636],[583,1471,1106],{"className":1472},[1105],[583,1474,1476],{"className":1475},[1042],[583,1477,1480],{"className":1478,"style":1479},[1046],"height:0.686em;",[583,1481],{},[583,1483],{"className":1484},[1119,1030],[583,1486,1488],{"className":1487,"style":1401},[1119,1400],[583,1489,1295],{"className":1490},[1405,1061],[565,1492,1493,1494,692],{},"Umgekehrt erhält man aus einem z-Wert den ursprünglichen Wert mit ",[583,1495,1497,1525],{"className":1496},[586],[583,1498,1500],{"className":1499},[590],[592,1501,1502],{"xmlns":594},[596,1503,1504,1522],{},[599,1505,1506,1508,1510,1512,1515,1517,1520],{},[602,1507,1292],{},[606,1509,608],{},[602,1511,675],{},[606,1513,1514],{},"+",[602,1516,604],{},[606,1518,1519],{},"⋅",[602,1521,942],{},[614,1523,1524],{"encoding":616},"x = \\mu + z \\cdot \\sigma",[583,1526,1528,1546,1565,1584],{"className":1527,"ariaHidden":622},[621],[583,1529,1531,1534,1537,1540,1543],{"className":1530},[626],[583,1532],{"className":1533,"style":631},[630],[583,1535,1292],{"className":1536},[635,636],[583,1538],{"className":1539,"style":642},[641],[583,1541,608],{"className":1542},[646],[583,1544],{"className":1545,"style":642},[641],[583,1547,1549,1553,1556,1559,1562],{"className":1548},[626],[583,1550],{"className":1551,"style":1552},[630],"height:0.7778em;vertical-align:-0.1944em;",[583,1554,675],{"className":1555},[635,636],[583,1557],{"className":1558,"style":1460},[641],[583,1560,1514],{"className":1561},[1098],[583,1563],{"className":1564,"style":1460},[641],[583,1566,1568,1572,1575,1578,1581],{"className":1567},[626],[583,1569],{"className":1570,"style":1571},[630],"height:0.4445em;",[583,1573,604],{"className":1574,"style":637},[635,636],[583,1576],{"className":1577,"style":1460},[641],[583,1579,1519],{"className":1580},[1098],[583,1582],{"className":1583,"style":1460},[641],[583,1585,1587,1590],{"className":1586},[626],[583,1588],{"className":1589,"style":631},[630],[583,1591,942],{"className":1592,"style":958},[635,636],[560,1594,1596],{"id":1595},"beispiele","Beispiele",[565,1598,1599,1600,1652,1653,1705,1706,1735],{},"Eine Klausur hat den Mittelwert ",[583,1601,1603,1622],{"className":1602},[586],[583,1604,1606],{"className":1605},[590],[592,1607,1608],{"xmlns":594},[596,1609,1610,1619],{},[599,1611,1612,1614,1616],{},[602,1613,675],{},[606,1615,608],{},[610,1617,1618],{},"70",[614,1620,1621],{"encoding":616},"\\mu = 70",[583,1623,1625,1643],{"className":1624,"ariaHidden":622},[621],[583,1626,1628,1631,1634,1637,1640],{"className":1627},[626],[583,1629],{"className":1630,"style":688},[630],[583,1632,675],{"className":1633},[635,636],[583,1635],{"className":1636,"style":642},[641],[583,1638,608],{"className":1639},[646],[583,1641],{"className":1642,"style":642},[641],[583,1644,1646,1649],{"className":1645},[626],[583,1647],{"className":1648,"style":656},[630],[583,1650,1618],{"className":1651},[635]," Punkte und die Standardabweichung ",[583,1654,1656,1675],{"className":1655},[586],[583,1657,1659],{"className":1658},[590],[592,1660,1661],{"xmlns":594},[596,1662,1663,1672],{},[599,1664,1665,1667,1669],{},[602,1666,942],{},[606,1668,608],{},[610,1670,1671],{},"8",[614,1673,1674],{"encoding":616},"\\sigma = 8",[583,1676,1678,1696],{"className":1677,"ariaHidden":622},[621],[583,1679,1681,1684,1687,1690,1693],{"className":1680},[626],[583,1682],{"className":1683,"style":631},[630],[583,1685,942],{"className":1686,"style":958},[635,636],[583,1688],{"className":1689,"style":642},[641],[583,1691,608],{"className":1692},[646],[583,1694],{"className":1695,"style":642},[641],[583,1697,1699,1702],{"className":1698},[626],[583,1700],{"className":1701,"style":656},[630],[583,1703,1671],{"className":1704},[635]," Punkte. Lea hat ",[583,1707,1709,1723],{"className":1708},[586],[583,1710,1712],{"className":1711},[590],[592,1713,1714],{"xmlns":594},[596,1715,1716,1721],{},[599,1717,1718],{},[610,1719,1720],{},"82",[614,1722,1720],{"encoding":616},[583,1724,1726],{"className":1725,"ariaHidden":622},[621],[583,1727,1729,1732],{"className":1728},[626],[583,1730],{"className":1731,"style":656},[630],[583,1733,1720],{"className":1734},[635]," Punkte:",[583,1737,1739],{"className":1738},[1264],[583,1740,1742,1775],{"className":1741},[586],[583,1743,1745],{"className":1744},[590],[592,1746,1747],{"xmlns":594,"display":1273},[596,1748,1749,1772],{},[599,1750,1751,1753,1755,1767,1769],{},[602,1752,604],{},[606,1754,608],{},[978,1756,1757,1765],{},[599,1758,1759,1761,1763],{},[610,1760,1720],{},[606,1762,986],{},[610,1764,1618],{},[610,1766,1671],{},[606,1768,608],{},[610,1770,1771],{},"1,5",[614,1773,1774],{"encoding":616},"z = \\frac{82 - 70}{8} = 1{,}5",[583,1776,1778,1796,1887],{"className":1777,"ariaHidden":622},[621],[583,1779,1781,1784,1787,1790,1793],{"className":1780},[626],[583,1782],{"className":1783,"style":631},[630],[583,1785,604],{"className":1786,"style":637},[635,636],[583,1788],{"className":1789,"style":642},[641],[583,1791,608],{"className":1792},[646],[583,1794],{"className":1795,"style":642},[641],[583,1797,1799,1803,1878,1881,1884],{"className":1798},[626],[583,1800],{"className":1801,"style":1802},[630],"height:2.0074em;vertical-align:-0.686em;",[583,1804,1806,1809,1875],{"className":1805},[635],[583,1807],{"className":1808},[1029,1030],[583,1810,1812],{"className":1811},[978],[583,1813,1815,1867],{"className":1814},[1037,1038],[583,1816,1818,1864],{"className":1817},[1042],[583,1819,1822,1833,1841],{"className":1820,"style":1821},[1046],"height:1.3214em;",[583,1823,1824,1827],{"style":1427},[583,1825],{"className":1826,"style":1055},[1054],[583,1828,1830],{"className":1829},[635],[583,1831,1671],{"className":1832},[635],[583,1834,1835,1838],{"style":1071},[583,1836],{"className":1837,"style":1055},[1054],[583,1839],{"className":1840,"style":1079},[1078],[583,1842,1843,1846],{"style":1447},[583,1844],{"className":1845,"style":1055},[1054],[583,1847,1849,1852,1855,1858,1861],{"className":1848},[635],[583,1850,1720],{"className":1851},[635],[583,1853],{"className":1854,"style":1460},[641],[583,1856,986],{"className":1857},[1098],[583,1859],{"className":1860,"style":1460},[641],[583,1862,1618],{"className":1863},[635],[583,1865,1106],{"className":1866},[1105],[583,1868,1870],{"className":1869},[1042],[583,1871,1873],{"className":1872,"style":1479},[1046],[583,1874],{},[583,1876],{"className":1877},[1119,1030],[583,1879],{"className":1880,"style":642},[641],[583,1882,608],{"className":1883},[646],[583,1885],{"className":1886,"style":642},[641],[583,1888,1890,1894,1897,1905],{"className":1889},[626],[583,1891],{"className":1892,"style":1893},[630],"height:0.8389em;vertical-align:-0.1944em;",[583,1895,1194],{"className":1896},[635],[583,1898,1900],{"className":1899},[635],[583,1901,1904],{"className":1902},[1903],"mpunct",",",[583,1906,1908],{"className":1907},[635],"5",[565,1910,1911,1912,1175,1964,2015,2016,2045,2046,2204],{},"In einer anderen Klausur (",[583,1913,1915,1934],{"className":1914},[586],[583,1916,1918],{"className":1917},[590],[592,1919,1920],{"xmlns":594},[596,1921,1922,1931],{},[599,1923,1924,1926,1928],{},[602,1925,675],{},[606,1927,608],{},[610,1929,1930],{},"65",[614,1932,1933],{"encoding":616},"\\mu = 65",[583,1935,1937,1955],{"className":1936,"ariaHidden":622},[621],[583,1938,1940,1943,1946,1949,1952],{"className":1939},[626],[583,1941],{"className":1942,"style":688},[630],[583,1944,675],{"className":1945},[635,636],[583,1947],{"className":1948,"style":642},[641],[583,1950,608],{"className":1951},[646],[583,1953],{"className":1954,"style":642},[641],[583,1956,1958,1961],{"className":1957},[626],[583,1959],{"className":1960,"style":656},[630],[583,1962,1930],{"className":1963},[635],[583,1965,1967,1985],{"className":1966},[586],[583,1968,1970],{"className":1969},[590],[592,1971,1972],{"xmlns":594},[596,1973,1974,1982],{},[599,1975,1976,1978,1980],{},[602,1977,942],{},[606,1979,608],{},[610,1981,1908],{},[614,1983,1984],{"encoding":616},"\\sigma = 5",[583,1986,1988,2006],{"className":1987,"ariaHidden":622},[621],[583,1989,1991,1994,1997,2000,2003],{"className":1990},[626],[583,1992],{"className":1993,"style":631},[630],[583,1995,942],{"className":1996,"style":958},[635,636],[583,1998],{"className":1999,"style":642},[641],[583,2001,608],{"className":2002},[646],[583,2004],{"className":2005,"style":642},[641],[583,2007,2009,2012],{"className":2008},[626],[583,2010],{"className":2011,"style":656},[630],[583,2013,1908],{"className":2014},[635],") hat Tom ",[583,2017,2019,2033],{"className":2018},[586],[583,2020,2022],{"className":2021},[590],[592,2023,2024],{"xmlns":594},[596,2025,2026,2031],{},[599,2027,2028],{},[610,2029,2030],{},"75",[614,2032,2030],{"encoding":616},[583,2034,2036],{"className":2035,"ariaHidden":622},[621],[583,2037,2039,2042],{"className":2038},[626],[583,2040],{"className":2041,"style":656},[630],[583,2043,2030],{"className":2044},[635]," Punkte, also ",[583,2047,2049,2082],{"className":2048},[586],[583,2050,2052],{"className":2051},[590],[592,2053,2054],{"xmlns":594},[596,2055,2056,2079],{},[599,2057,2058,2060,2062,2074,2076],{},[602,2059,604],{},[606,2061,608],{},[978,2063,2064,2072],{},[599,2065,2066,2068,2070],{},[610,2067,2030],{},[606,2069,986],{},[610,2071,1930],{},[610,2073,1908],{},[606,2075,608],{},[610,2077,2078],{},"2",[614,2080,2081],{"encoding":616},"z = \\frac{75 - 65}{5} = 2",[583,2083,2085,2103,2195],{"className":2084,"ariaHidden":622},[621],[583,2086,2088,2091,2094,2097,2100],{"className":2087},[626],[583,2089],{"className":2090,"style":631},[630],[583,2092,604],{"className":2093,"style":637},[635,636],[583,2095],{"className":2096,"style":642},[641],[583,2098,608],{"className":2099},[646],[583,2101],{"className":2102,"style":642},[641],[583,2104,2106,2110,2186,2189,2192],{"className":2105},[626],[583,2107],{"className":2108,"style":2109},[630],"height:1.1901em;vertical-align:-0.345em;",[583,2111,2113,2116,2183],{"className":2112},[635],[583,2114],{"className":2115},[1029,1030],[583,2117,2119],{"className":2118},[978],[583,2120,2122,2175],{"className":2121},[1037,1038],[583,2123,2125,2172],{"className":2124},[1042],[583,2126,2129,2143,2151],{"className":2127,"style":2128},[1046],"height:0.8451em;",[583,2130,2131,2134],{"style":1050},[583,2132],{"className":2133,"style":1055},[1054],[583,2135,2137],{"className":2136},[1059,1060,1061,1062],[583,2138,2140],{"className":2139},[635,1062],[583,2141,1908],{"className":2142},[635,1062],[583,2144,2145,2148],{"style":1071},[583,2146],{"className":2147,"style":1055},[1054],[583,2149],{"className":2150,"style":1079},[1078],[583,2152,2154,2157],{"style":2153},"top:-3.394em;",[583,2155],{"className":2156,"style":1055},[1054],[583,2158,2160],{"className":2159},[1059,1060,1061,1062],[583,2161,2163,2166,2169],{"className":2162},[635,1062],[583,2164,2030],{"className":2165},[635,1062],[583,2167,986],{"className":2168},[1098,1062],[583,2170,1930],{"className":2171},[635,1062],[583,2173,1106],{"className":2174},[1105],[583,2176,2178],{"className":2177},[1042],[583,2179,2181],{"className":2180,"style":1113},[1046],[583,2182],{},[583,2184],{"className":2185},[1119,1030],[583,2187],{"className":2188,"style":642},[641],[583,2190,608],{"className":2191},[646],[583,2193],{"className":2194,"style":642},[641],[583,2196,2198,2201],{"className":2197},[626],[583,2199],{"className":2200,"style":656},[630],[583,2202,2078],{"className":2203},[635],". Im Vergleich zu den jeweiligen Mitschreibenden hat Tom besser abgeschnitten, obwohl er weniger Punkte hat.",[565,2206,2207,2208,2295,2296,2339,2340,692],{},"Sind die Punkte normalverteilt, liegt Lea vor etwa ",[583,2209,2211,2237],{"className":2210},[586],[583,2212,2214],{"className":2213},[590],[592,2215,2216],{"xmlns":594},[596,2217,2218,2234],{},[599,2219,2220,2222,2224,2226,2228,2231],{},[602,2221,1244],{"mathvariant":1243},[606,2223,1284],{"stretchy":1283},[610,2225,1771],{},[606,2227,1295],{"stretchy":1283},[606,2229,2230],{},"≈",[610,2232,2233],{},"0,9332",[614,2235,2236],{"encoding":616},"\\Phi(1{,}5) \\approx 0{,}9332",[583,2238,2240,2276],{"className":2239,"ariaHidden":622},[621],[583,2241,2243,2246,2249,2252,2255,2261,2264,2267,2270,2273],{"className":2242},[626],[583,2244],{"className":2245,"style":1334},[630],[583,2247,1244],{"className":2248},[635],[583,2250,1284],{"className":2251},[1029],[583,2253,1194],{"className":2254},[635],[583,2256,2258],{"className":2257},[635],[583,2259,1904],{"className":2260},[1903],[583,2262,1908],{"className":2263},[635],[583,2265,1295],{"className":2266},[1119],[583,2268],{"className":2269,"style":642},[641],[583,2271,2230],{"className":2272},[646],[583,2274],{"className":2275,"style":642},[641],[583,2277,2279,2282,2285,2291],{"className":2278},[626],[583,2280],{"className":2281,"style":1893},[630],[583,2283,612],{"className":2284},[635],[583,2286,2288],{"className":2287},[635],[583,2289,1904],{"className":2290},[1903],[583,2292,2294],{"className":2293},[635],"9332",", also gut ",[583,2297,2299,2320],{"className":2298},[586],[583,2300,2302],{"className":2301},[590],[592,2303,2304],{"xmlns":594},[596,2305,2306,2317],{},[599,2307,2308,2311,2314],{},[610,2309,2310],{},"93",[1301,2312,2313],{}," ",[602,2315,2316],{"mathvariant":1243},"%",[614,2318,2319],{"encoding":616},"93\\,\\%",[583,2321,2323],{"className":2322,"ariaHidden":622},[621],[583,2324,2326,2330,2333,2336],{"className":2325},[626],[583,2327],{"className":2328,"style":2329},[630],"height:0.8056em;vertical-align:-0.0556em;",[583,2331,2310],{"className":2332},[635],[583,2334],{"className":2335,"style":1392},[641],[583,2337,2316],{"className":2338},[635]," aller Ergebnisse. Ein Ergebnis über Toms Wert hat nur die Wahrscheinlichkeit ",[583,2341,2343,2372],{"className":2342},[586],[583,2344,2346],{"className":2345},[590],[592,2347,2348],{"xmlns":594},[596,2349,2350,2369],{},[599,2351,2352,2354,2356,2358,2360,2362,2364,2366],{},[610,2353,1194],{},[606,2355,986],{},[602,2357,1244],{"mathvariant":1243},[606,2359,1284],{"stretchy":1283},[610,2361,2078],{},[606,2363,1295],{"stretchy":1283},[606,2365,2230],{},[610,2367,2368],{},"0,0228",[614,2370,2371],{"encoding":616},"1 - \\Phi(2) \\approx 0{,}0228",[583,2373,2375,2394,2421],{"className":2374,"ariaHidden":622},[621],[583,2376,2378,2382,2385,2388,2391],{"className":2377},[626],[583,2379],{"className":2380,"style":2381},[630],"height:0.7278em;vertical-align:-0.0833em;",[583,2383,1194],{"className":2384},[635],[583,2386],{"className":2387,"style":1460},[641],[583,2389,986],{"className":2390},[1098],[583,2392],{"className":2393,"style":1460},[641],[583,2395,2397,2400,2403,2406,2409,2412,2415,2418],{"className":2396},[626],[583,2398],{"className":2399,"style":1334},[630],[583,2401,1244],{"className":2402},[635],[583,2404,1284],{"className":2405},[1029],[583,2407,2078],{"className":2408},[635],[583,2410,1295],{"className":2411},[1119],[583,2413],{"className":2414,"style":642},[641],[583,2416,2230],{"className":2417},[646],[583,2419],{"className":2420,"style":642},[641],[583,2422,2424,2427,2430,2436],{"className":2423},[626],[583,2425],{"className":2426,"style":1893},[630],[583,2428,612],{"className":2429},[635],[583,2431,2433],{"className":2432},[635],[583,2434,1904],{"className":2435},[1903],[583,2437,2439],{"className":2438},[635],"0228",[565,2441,2442,2443,927,2495,2547,2548,2614,2615,692],{},"Rückrechnung: Bei ",[583,2444,2446,2465],{"className":2445},[586],[583,2447,2449],{"className":2448},[590],[592,2450,2451],{"xmlns":594},[596,2452,2453,2462],{},[599,2454,2455,2457,2459],{},[602,2456,675],{},[606,2458,608],{},[610,2460,2461],{},"100",[614,2463,2464],{"encoding":616},"\\mu = 100",[583,2466,2468,2486],{"className":2467,"ariaHidden":622},[621],[583,2469,2471,2474,2477,2480,2483],{"className":2470},[626],[583,2472],{"className":2473,"style":688},[630],[583,2475,675],{"className":2476},[635,636],[583,2478],{"className":2479,"style":642},[641],[583,2481,608],{"className":2482},[646],[583,2484],{"className":2485,"style":642},[641],[583,2487,2489,2492],{"className":2488},[626],[583,2490],{"className":2491,"style":656},[630],[583,2493,2461],{"className":2494},[635],[583,2496,2498,2517],{"className":2497},[586],[583,2499,2501],{"className":2500},[590],[592,2502,2503],{"xmlns":594},[596,2504,2505,2514],{},[599,2506,2507,2509,2511],{},[602,2508,942],{},[606,2510,608],{},[610,2512,2513],{},"15",[614,2515,2516],{"encoding":616},"\\sigma = 15",[583,2518,2520,2538],{"className":2519,"ariaHidden":622},[621],[583,2521,2523,2526,2529,2532,2535],{"className":2522},[626],[583,2524],{"className":2525,"style":631},[630],[583,2527,942],{"className":2528,"style":958},[635,636],[583,2530],{"className":2531,"style":642},[641],[583,2533,608],{"className":2534},[646],[583,2536],{"className":2537,"style":642},[641],[583,2539,2541,2544],{"className":2540},[626],[583,2542],{"className":2543,"style":656},[630],[583,2545,2513],{"className":2546},[635]," gehört zu ",[583,2549,2551,2572],{"className":2550},[586],[583,2552,2554],{"className":2553},[590],[592,2555,2556],{"xmlns":594},[596,2557,2558,2569],{},[599,2559,2560,2562,2564,2566],{},[602,2561,604],{},[606,2563,608],{},[606,2565,986],{},[610,2567,2568],{},"1,2",[614,2570,2571],{"encoding":616},"z = -1{,}2",[583,2573,2575,2593],{"className":2574,"ariaHidden":622},[621],[583,2576,2578,2581,2584,2587,2590],{"className":2577},[626],[583,2579],{"className":2580,"style":631},[630],[583,2582,604],{"className":2583,"style":637},[635,636],[583,2585],{"className":2586,"style":642},[641],[583,2588,608],{"className":2589},[646],[583,2591],{"className":2592,"style":642},[641],[583,2594,2596,2599,2602,2605,2611],{"className":2595},[626],[583,2597],{"className":2598,"style":1893},[630],[583,2600,986],{"className":2601},[635],[583,2603,1194],{"className":2604},[635],[583,2606,2608],{"className":2607},[635],[583,2609,1904],{"className":2610},[1903],[583,2612,2078],{"className":2613},[635]," der Wert ",[583,2616,2618,2654],{"className":2617},[586],[583,2619,2621],{"className":2620},[590],[592,2622,2623],{"xmlns":594},[596,2624,2625,2651],{},[599,2626,2627,2629,2631,2633,2635,2637,2639,2641,2643,2645,2647,2649],{},[602,2628,1292],{},[606,2630,608],{},[610,2632,2461],{},[606,2634,1514],{},[606,2636,1284],{"stretchy":1283},[606,2638,986],{},[610,2640,2568],{},[606,2642,1295],{"stretchy":1283},[606,2644,1519],{},[610,2646,2513],{},[606,2648,608],{},[610,2650,1720],{},[614,2652,2653],{"encoding":616},"x = 100 + (-1{,}2) \\cdot 15 = 82",[583,2655,2657,2675,2693,2729,2747],{"className":2656,"ariaHidden":622},[621],[583,2658,2660,2663,2666,2669,2672],{"className":2659},[626],[583,2661],{"className":2662,"style":631},[630],[583,2664,1292],{"className":2665},[635,636],[583,2667],{"className":2668,"style":642},[641],[583,2670,608],{"className":2671},[646],[583,2673],{"className":2674,"style":642},[641],[583,2676,2678,2681,2684,2687,2690],{"className":2677},[626],[583,2679],{"className":2680,"style":2381},[630],[583,2682,2461],{"className":2683},[635],[583,2685],{"className":2686,"style":1460},[641],[583,2688,1514],{"className":2689},[1098],[583,2691],{"className":2692,"style":1460},[641],[583,2694,2696,2699,2702,2705,2708,2714,2717,2720,2723,2726],{"className":2695},[626],[583,2697],{"className":2698,"style":1334},[630],[583,2700,1284],{"className":2701},[1029],[583,2703,986],{"className":2704},[635],[583,2706,1194],{"className":2707},[635],[583,2709,2711],{"className":2710},[635],[583,2712,1904],{"className":2713},[1903],[583,2715,2078],{"className":2716},[635],[583,2718,1295],{"className":2719},[1119],[583,2721],{"className":2722,"style":1460},[641],[583,2724,1519],{"className":2725},[1098],[583,2727],{"className":2728,"style":1460},[641],[583,2730,2732,2735,2738,2741,2744],{"className":2731},[626],[583,2733],{"className":2734,"style":656},[630],[583,2736,2513],{"className":2737},[635],[583,2739],{"className":2740,"style":642},[641],[583,2742,608],{"className":2743},[646],[583,2745],{"className":2746,"style":642},[641],[583,2748,2750,2753],{"className":2749},[626],[583,2751],{"className":2752,"style":656},[630],[583,2754,1720],{"className":2755},[635],[560,2757,2759],{"id":2758},"typische-fehler","Typische Fehler",[577,2761,2762,2910,2994],{},[580,2763,2764,2765,2909],{},"Durch die Varianz statt durch die Standardabweichung teilen. ",[583,2766,2768,2798],{"className":2767},[586],[583,2769,2771],{"className":2770},[590],[592,2772,2773],{"xmlns":594},[596,2774,2775,2795],{},[599,2776,2777,2790,2792],{},[978,2778,2779,2787],{},[599,2780,2781,2783,2785],{},[610,2782,1720],{},[606,2784,986],{},[610,2786,1618],{},[610,2788,2789],{},"64",[606,2791,608],{},[610,2793,2794],{},"0,1875",[614,2796,2797],{"encoding":616},"\\frac{82 - 70}{64} = 0{,}1875",[583,2799,2801,2890],{"className":2800,"ariaHidden":622},[621],[583,2802,2804,2807,2881,2884,2887],{"className":2803},[626],[583,2805],{"className":2806,"style":2109},[630],[583,2808,2810,2813,2878],{"className":2809},[635],[583,2811],{"className":2812},[1029,1030],[583,2814,2816],{"className":2815},[978],[583,2817,2819,2870],{"className":2818},[1037,1038],[583,2820,2822,2867],{"className":2821},[1042],[583,2823,2825,2839,2847],{"className":2824,"style":2128},[1046],[583,2826,2827,2830],{"style":1050},[583,2828],{"className":2829,"style":1055},[1054],[583,2831,2833],{"className":2832},[1059,1060,1061,1062],[583,2834,2836],{"className":2835},[635,1062],[583,2837,2789],{"className":2838},[635,1062],[583,2840,2841,2844],{"style":1071},[583,2842],{"className":2843,"style":1055},[1054],[583,2845],{"className":2846,"style":1079},[1078],[583,2848,2849,2852],{"style":2153},[583,2850],{"className":2851,"style":1055},[1054],[583,2853,2855],{"className":2854},[1059,1060,1061,1062],[583,2856,2858,2861,2864],{"className":2857},[635,1062],[583,2859,1720],{"className":2860},[635,1062],[583,2862,986],{"className":2863},[1098,1062],[583,2865,1618],{"className":2866},[635,1062],[583,2868,1106],{"className":2869},[1105],[583,2871,2873],{"className":2872},[1042],[583,2874,2876],{"className":2875,"style":1113},[1046],[583,2877],{},[583,2879],{"className":2880},[1119,1030],[583,2882],{"className":2883,"style":642},[641],[583,2885,608],{"className":2886},[646],[583,2888],{"className":2889,"style":642},[641],[583,2891,2893,2896,2899,2905],{"className":2892},[626],[583,2894],{"className":2895,"style":1893},[630],[583,2897,612],{"className":2898},[635],[583,2900,2902],{"className":2901},[635],[583,2903,1904],{"className":2904},[1903],[583,2906,2908],{"className":2907},[635],"1875"," ist falsch.",[580,2911,2912,2913,2964,2965,2993],{},"Die Reihenfolge im Zähler vertauschen (",[583,2914,2916,2934],{"className":2915},[586],[583,2917,2919],{"className":2918},[590],[592,2920,2921],{"xmlns":594},[596,2922,2923,2931],{},[599,2924,2925,2927,2929],{},[602,2926,675],{},[606,2928,986],{},[602,2930,1292],{},[614,2932,2933],{"encoding":616},"\\mu - x",[583,2935,2937,2955],{"className":2936,"ariaHidden":622},[621],[583,2938,2940,2943,2946,2949,2952],{"className":2939},[626],[583,2941],{"className":2942,"style":1552},[630],[583,2944,675],{"className":2945},[635,636],[583,2947],{"className":2948,"style":1460},[641],[583,2950,986],{"className":2951},[1098],[583,2953],{"className":2954,"style":1460},[641],[583,2956,2958,2961],{"className":2957},[626],[583,2959],{"className":2960,"style":631},[630],[583,2962,1292],{"className":2963},[635,636],"). Dann stimmt das Vorzeichen nicht, und ",[583,2966,2968,2981],{"className":2967},[586],[583,2969,2971],{"className":2970},[590],[592,2972,2973],{"xmlns":594},[596,2974,2975,2979],{},[599,2976,2977],{},[602,2978,1244],{"mathvariant":1243},[614,2980,1247],{"encoding":616},[583,2982,2984],{"className":2983,"ariaHidden":622},[621],[583,2985,2987,2990],{"className":2986},[626],[583,2988],{"className":2989,"style":893},[630],[583,2991,1244],{"className":2992},[635]," liefert den falschen Wert.",[580,2995,2996,3040,3041,3084,3085,3151,3152,692],{},[583,2997,2999,3019],{"className":2998},[586],[583,3000,3002],{"className":3001},[590],[592,3003,3004],{"xmlns":594},[596,3005,3006,3016],{},[599,3007,3008,3010,3012,3014],{},[602,3009,1244],{"mathvariant":1243},[606,3011,1284],{"stretchy":1283},[602,3013,604],{},[606,3015,1295],{"stretchy":1283},[614,3017,3018],{"encoding":616},"\\Phi(z)",[583,3020,3022],{"className":3021,"ariaHidden":622},[621],[583,3023,3025,3028,3031,3034,3037],{"className":3024},[626],[583,3026],{"className":3027,"style":1334},[630],[583,3029,1244],{"className":3030},[635],[583,3032,1284],{"className":3033},[1029],[583,3035,604],{"className":3036,"style":637},[635,636],[583,3038,1295],{"className":3039},[1119]," als Wahrscheinlichkeit für „größer als“ lesen. ",[583,3042,3044,3063],{"className":3043},[586],[583,3045,3047],{"className":3046},[590],[592,3048,3049],{"xmlns":594},[596,3050,3051,3061],{},[599,3052,3053,3055,3057,3059],{},[602,3054,1244],{"mathvariant":1243},[606,3056,1284],{"stretchy":1283},[602,3058,604],{},[606,3060,1295],{"stretchy":1283},[614,3062,3018],{"encoding":616},[583,3064,3066],{"className":3065,"ariaHidden":622},[621],[583,3067,3069,3072,3075,3078,3081],{"className":3068},[626],[583,3070],{"className":3071,"style":1334},[630],[583,3073,1244],{"className":3074},[635],[583,3076,1284],{"className":3077},[1029],[583,3079,604],{"className":3080,"style":637},[635,636],[583,3082,1295],{"className":3083},[1119]," ist immer ",[583,3086,3088,3112],{"className":3087},[586],[583,3089,3091],{"className":3090},[590],[592,3092,3093],{"xmlns":594},[596,3094,3095,3109],{},[599,3096,3097,3099,3101,3103,3105,3107],{},[602,3098,1280],{},[606,3100,1284],{"stretchy":1283},[602,3102,974],{},[606,3104,1289],{},[602,3106,604],{},[606,3108,1295],{"stretchy":1283},[614,3110,3111],{"encoding":616},"P(Z \\leq z)",[583,3113,3115,3139],{"className":3114,"ariaHidden":622},[621],[583,3116,3118,3121,3124,3127,3130,3133,3136],{"className":3117},[626],[583,3119],{"className":3120,"style":1334},[630],[583,3122,1280],{"className":3123,"style":1338},[635,636],[583,3125,1284],{"className":3126},[1029],[583,3128,974],{"className":3129,"style":1006},[635,636],[583,3131],{"className":3132,"style":642},[641],[583,3134,1289],{"className":3135},[646],[583,3137],{"className":3138,"style":642},[641],[583,3140,3142,3145,3148],{"className":3141},[626],[583,3143],{"className":3144,"style":1334},[630],[583,3146,604],{"className":3147,"style":637},[635,636],[583,3149,1295],{"className":3150},[1119],"; für „größer“ rechnet man ",[583,3153,3155,3179],{"className":3154},[586],[583,3156,3158],{"className":3157},[590],[592,3159,3160],{"xmlns":594},[596,3161,3162,3176],{},[599,3163,3164,3166,3168,3170,3172,3174],{},[610,3165,1194],{},[606,3167,986],{},[602,3169,1244],{"mathvariant":1243},[606,3171,1284],{"stretchy":1283},[602,3173,604],{},[606,3175,1295],{"stretchy":1283},[614,3177,3178],{"encoding":616},"1 - \\Phi(z)",[583,3180,3182,3200],{"className":3181,"ariaHidden":622},[621],[583,3183,3185,3188,3191,3194,3197],{"className":3184},[626],[583,3186],{"className":3187,"style":2381},[630],[583,3189,1194],{"className":3190},[635],[583,3192],{"className":3193,"style":1460},[641],[583,3195,986],{"className":3196},[1098],[583,3198],{"className":3199,"style":1460},[641],[583,3201,3203,3206,3209,3212,3215],{"className":3202},[626],[583,3204],{"className":3205,"style":1334},[630],[583,3207,1244],{"className":3208},[635],[583,3210,1284],{"className":3211},[1029],[583,3213,604],{"className":3214,"style":637},[635,636],[583,3216,1295],{"className":3217},[1119],{"title":3219,"searchDepth":3220,"depth":3220,"links":3221},"",2,[3222,3223,3224],{"id":562,"depth":3220,"text":563},{"id":1595,"depth":3220,"text":1596},{"id":2758,"depth":3220,"text":2759},[3226,3228,3231,3233,3236,3239,3241],{"lhs":3227,"rhs":1292},"u + ((x - u)\u002Fs) * s",{"lhs":3229,"rhs":3230},"(82 - 70) \u002F 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style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":945,"meaning":3279,"symbolHtml":3280},"Standardabweichung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>σ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sigma\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\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","WYEFprEwJoN-joTVromwUEhU4TZZQaf8quIighCH6LI",[3283,3286,3289],{"stem":3284,"title":3285,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fnormalverteilung","Normalverteilung",{"stem":3287,"title":3288,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fsigma-regeln","Sigma-Regeln",{"stem":3290,"title":3279,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstandardabweichung",1793824287786]