Statistical Analysis of the Ages of Noah's MALE Ancestors and a Probabilistic Proof That Enoch's Premature Death was Indeed an Act of God By Shalosh B. Ekhad According to Bereshit Perek Heh (Genesis Ch. 5), the line of Male first-born\ s, from Adam all the way to Noah were Adam, Seth, Enosh, Kenan, Mahalalel, Jared, Enoch, Methuselah, Lamech, Noah Their ages when their first sons were born were as follows Adam, begat , Seth, at the age of , 130 Seth, begat , Enosh, at the age of , 105 Enosh, begat , Kenan, at the age of , 90 Kenan, begat , Mahalalel, at the age of , 70 Mahalalel, begat , Jared, at the age of , 65 Jared, begat , Enoch, at the age of , 162 Enoch, begat , Methuselah, at the age of , 65 Methuselah, begat , Lamech, at the age of , 187 Lamech, begat , Noah, at the age of , 182 Noah begat Shem, Ham and Japhet (a triplet(?)) at the age of, 500 The average age at the birth of the first son amongst these ten men is 155.6000000 The standard deviation is 123.1253020 The skewness (alias standarized third moment) is 2.054912096 The kurtosis (alias standarized fourth moment) is 6.215305947 The , 5, -th standarized moment is, 17.05823471 The , 6, -th standarized moment is, 47.94138628 The , 7, -th standarized moment is, 133.9383911 The , 8, -th standarized moment is, 374.7604637 The , 9, -th standarized moment is, 1048.179195 The , 10, -th standarized moment is, 2931.974158 ---------------------------------------------------- Now let's study the number of years from the birth of the first-born-son to \ death Adam, lived after the birth of, Seth, an additional , 800, years. Seth, lived after the birth of, Enosh, an additional , 807, years. Enosh, lived after the birth of, Kenan, an additional , 815, years. Kenan, lived after the birth of, Mahalalel, an additional , 840, years. Mahalalel, lived after the birth of, Jared, an additional , 830, years. Jared, lived after the birth of, Enoch, an additional , 800, years. Enoch, lived after the birth of, Methuselah, an additional , 300, years. Methuselah, lived after the birth of, Lamech, an additional , 782, years. Lamech, lived after the birth of, Noah, an additional , 595, years. Noah lived, after the birth of his three sons, 450, years. The average of the remaining years is 701.9000000 The standard deviation is 179.2726694 The skewness (alias standarized third moment) is -1.256186724 The kurtosis (alias standarized fourth moment) is 3.039210145 The , 5, -th standarized moment is, -6.143654108 The , 6, -th standarized moment is, 13.51959991 The , 7, -th standarized moment is, -29.50836213 The , 8, -th standarized moment is, 65.34757909 The , 9, -th standarized moment is, -145.1510180 The , 10, -th standarized moment is, 323.6694046 Note that it is not far from normal --------------------------------------- Now let's study the total number of years lived, i.e., age at death Adam, died at the age of , 930, years. Seth, died at the age of , 912, years. Enosh, died at the age of , 905, years. Kenan, died at the age of , 910, years. Mahalalel, died at the age of , 895, years. Jared, died at the age of , 962, years. Enoch, died at the age of , 365, years. Methuselah, died at the age of , 969, years. Lamech, died at the age of , 777, years. Noah, died at the age of , 950, years. The average of the age-at-death is 857.5000000 The standard deviation is 171.9274556 The skewness (alias standarized third moment) is -2.278905012 The kurtosis (alias standarized fourth moment) is 6.783921958 The , 5, -th standarized moment is, -19.26463547 The , 6, -th standarized moment is, 55.27105017 The , 7, -th standarized moment is, -158.2713361 The , 8, -th standarized moment is, 453.4128060 The , 9, -th standarized moment is, -1298.816584 The , 10, -th standarized moment is, 3720.576628 ---------------------------------------- Since Enoch is definitely an outlier, let's study the respective statistics \ without him The average age at the birth of the first son amongst these nine men (i.e. n\ ot including Enoch) is 165.6666667 The standard deviation is 125.8208603 The skewness (alias standarized third moment) is 1.940558862 The kurtosis (alias standarized fourth moment) is 5.643481087 The , 5, -th standarized moment is, 14.64300346 The , 6, -th standarized moment is, 39.17019392 The , 7, -th standarized moment is, 103.8878868 The , 8, -th standarized moment is, 276.2015262 The , 9, -th standarized moment is, 733.8132567 The , 10, -th standarized moment is, 1949.989162 ---------------------------------------------------- Now let's study the number of years from the birth of the first-born-son to \ death (not counting Enoch) The average of the remaining years is 746.5555556 The standard deviation is 125.5725652 The skewness (alias standarized third moment) is -1.530429495 The kurtosis (alias standarized fourth moment) is 3.771493754 The , 5, -th standarized moment is, -8.395596433 The , 6, -th standarized moment is, 19.65389359 The , 7, -th standarized moment is, -45.91484296 The , 8, -th standarized moment is, 108.0260930 The , 9, -th standarized moment is, -254.4903689 The , 10, -th standarized moment is, 600.3489078 Note that it is not far from normal --------------------------------------- Now let's study the total number of years lived, i.e., age at death (not cou\ nting Enoch) The average of the age-at-death is 912.2222222 The standard deviation is 53.83468064 The skewness (alias standarized third moment) is -1.504152764 The kurtosis (alias standarized fourth moment) is 4.670997046 The , 5, -th standarized moment is, -10.87025711 The , 6, -th standarized moment is, 28.14031023 The , 7, -th standarized moment is, -69.85567017 The , 8, -th standarized moment is, 176.2896228 The , 9, -th standarized moment is, -441.9734509 The , 10, -th standarized moment is, 1110.994317 ---------------------------------------- Finally, let's see how unlikely it is for Enoch to die so young, at the tend\ er age of 365 years assuming a normal distibution (this assumption is reasonable, since the samp\ le is small and the standarized moments are not that far from 0,3,0,15, \ ...) Since the average is, 912.2222222, and the standard deviation (without correction for small samples) is, 53.83468064 -23 The prob. of dying at the age of 365 or less is, 0.1422589981 10 This took, 0.254, seconds.