Question

A company for dishwashers produces them such that only 1% are defective. If the dishwashers are independent, what are the mean and variance of the number of dishwashers that should be produced if the company wants the last dishwasher produced to be only the fourth defective? cross out cross out Select one: a. Mean = 100; Variance = 9900 O b. Mean = 400; Variance = 9900 c. Mean = 400; Variance = 39600 d. Mean = 100; Variance = 100 o e. Mean = 400; Variance = 400 cross out cross out cross out

Answer 1

If X: No of dishwashers that should be produced. X follows negative binomial distribution with parameter, r = 4 and p = 1% = 0.01

So, mean = r/p = 4/0.01 = 400

Variance = r(1-p)/p² = (4•0.99)/(0.01)² = 3.96/0.0001 = 39600