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P[X < 2] = (0.95)20(0.05)0 + 20(0.95)19(0.05) + 190(0.95)18(0.05)2 = 0.358 + 0.377 + 0.189 = 0.9245. | P[X < 2] = (0.95)20(0.05)0 + 20(0.95)19(0.05) + 190(0.95)18(0.05)2 = 0.358 + 0.377 + 0.189 = 0.9245. | ||
{{soacopyright | 2023}} | |||
Latest revision as of 21:05, 3 May 2023
Solution: E
Let X be the number of hurricanes over the 20-year period. The conditions of the problem give x is a binomial distribution with n = 20 and p = 0.05 . It follows that
P[X < 2] = (0.95)20(0.05)0 + 20(0.95)19(0.05) + 190(0.95)18(0.05)2 = 0.358 + 0.377 + 0.189 = 0.9245.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.