Question

5. Many cell phone service providers offer family plans wherein parents who subscribe can get discounts for other family members. Suppose that the number of cell phones per family is Poisson distributed with a mean of 1.5. If one family is randomly selected, calculate the following probabilities

a) Family has only 1 cell phone.

b) Family has 3 or more cell phones.

c) Family has 4 or fewer cell phones.

Answer 1

Solution:

Given:  X = the number of cell phones per family is Poisson distributed with a mean of 1.5.

That is:

Probability Mass function is :

We have to find the following probabilities:

Part a)

P( Family has only 1 cell phone ) = ..........?

That is:

P( X = 1 ) = .............?

Use Excel or Scientific calculator to find e^-1.5

Thus we get:

e^-1.5 = 0.22313

Thus

Part b)  

P( Family has 3 or more cell phones ) =...........?

Part c)

P( Family has 4 or fewer cell phones) =.........?