Suppose the number of presents that Santa Clause leaves under Christmas trees is Poisson distributed with a mean of 4.7 presents per house.

Question

Suppose the number of presents that Santa Clause leaves under Christmas trees is Poisson distributed with a mean of 4.7 presents per house.

A) Find the probability that he leaves exactly five presents under a tree

B) Find the probability that he leaves three or four presents under a tree.

C) Find the probability that he leaves at least three presents under a tree

Answer 1

Using the TI-84 (or you can use Poisson.dist in excel)

P(X=5) = Poissonpdf(4.7,5) = 0.1738

P(X=3) + P(X=4) = Poissonpdf(4.7,3) + Poissonpdf(4.7,4) = 0.1574 + 0.1849 = 0.3423

P(X>=3) = 1-P(X<=2) = 1 - Poissoncdf(4.7,2) = 1 - 0.1523 = 0.8477