raw materials are studied for contamination. suppose that the number of particles of contamination per pound of the material is a poisson random varable with a mean of 0.01 paterical per pounda) what is the expected number of pounds of material requried to obtain 15 particles of contamination? b) what is the standard deviation of the per pounds pf material required to obtain 15 particales of contamination?

A = 1500; B=387.3

Step-by-step explanation:

A. the expected number of pounds of material requried to obtain 15 particles of contamination

We represent:

Y as the poisson random variable with λ to be 0.01

X as Erlang random variable with r to be 15 particles

Therefore

E (X) = r/λ

= 15/0.01

=1500

B. standard deviation of the per pounds pf material required to obtain 15 particales of contamination

Standard deviation X = √ r/λ^2

√ 15/0.0001

=387.3