Question

7. A quality control engineer samples five from a large lot of manufactured firing pins and checks for defects. Unknown to the inspector, three of the five sampled firing pins are defective. The engineer will test the five pins in a randomly selected order until a defective is observed in which case the entire lot will be rejected). Let Y be the number of firing pins the quality control engineer must test. a) Find the probability distribution of Y. b) Suppose the cost of testing a single firing pin is $200. What is the expected cost of inspecting the lot?

Answer 1

P( defective)= 3/5=p

so, q=1- (3/5) = 2/5

Y be the number of firing pins the quality control engineer must test

a) Y~ geometric ( 3/5)

b) E(Y) = q/p = (2/5) / (3/5) = 2/3

So , exepected cost of inspecting the lot = 200 * (2/3) = 133.33