4.8.4 Raw materials are studied for contamination. Suppose that the number of particles of contamination per pound of material is a Poisson random variable with a mean of 0.02 particle per pound. Round the answers to the nearest integer. (a) What is the expected number of pounds of material required to obtain 14 particles of contamination? Enter your answer in accordance to the item a) of the question statement (b) What is the standard deviation of the pounds of materials required to obtain 14 particles of contamination?

Given that raw materials are studied for contamination. Suppose that the number of particles of contamination per pound of material is a Poisson random variable with a mean of 0.02 particle per pound.

a) To get 14 particles of contamination we must have

expected number of pounds = [tex]\frac{14}{0.02} \\=700[/tex]

b) Since for 700 pounds particles expected are 14 we can say in a Poisson distribution mean and variance are equal

i.e. Var (700 lbs to obtain 14 particles of contamination ) = 14

Std deviation =[tex]\sqrt{14} =3.742[/tex]