One of PoissonSolutionlamba 324 8 dPk

One of Poisson

Solution

lamba = 3.2/4 = .8

d)P(k<=0) = e^-.8(.8⁰/0!) = 0.4493289641172216

expected = 4*0.4493289641172216 = 1.7973158564688864accidents

c)P(k<=2) = e^-.8(.8⁰/0!+.8¹/1!+.8²/2!) =  0.9525774039285097

expected = 4*0.9525774039285097 = 3.8103096157140388accidents

b)P(k<=10) = e^-.8(.8⁰/0!+.8¹/1!+.8²/2!+.8³/3!+.8⁴/4!+.8⁵/5!+.8⁶/6!+.8⁷/7!+.8⁸/8!+.8⁹/9!+.8¹⁰/10!) = 0.9999999989643932

expected = 4*0.9999999989643932 = 3.9999999958575728accidents

a)P(k<=8) = e^-.8(.8⁰/0!+.8¹/1!+.8²/2!+.8³/3!+.8⁴/4!+.8⁵/5!+.8⁶/6!+.8⁷/7!+.8⁸/8!) = 0.9999998194765579

expected = 4*0.9999998194765579 = 3.9999992779062316accidents