Please show all work and explanation to Receive FULL CREDIT

Please show all work and explanation to Receive FULL CREDIT!!!

You are testing each product out of a particular product run. Historically, the probability of a defective product is 2%. You are asked to test samples from the product run until a defective product is found.

a. What is the probability distribution for Y?

b. What is the mean and standard deviation for Y?

c. What is the probability that you will find a defective product by the 3^rd draw?

Solution

a. What is the probability distribution for Y?

Geometric distribution with p=0.02

--------------------------------------------------------------------------------------------------------------------

b. What is the mean and standard deviation for Y?

mean=1/p=1/0.02=50

standard deviation =sqrt((1-p)/p^2)=sqrt((1-0.02)/0.02^2) =49.49747

--------------------------------------------------------------------------------------------------------------------

c. What is the probability that you will find a defective product by the 3^rd draw?

(1-0.02)^2*0.02 =0.019208