QUESTION 1

Suppose that when a new machine is functioning well, 92% of the items produced are non- defective. Assume that a random sample of five parts produced on the machine is selected and we are interested in the number of defective parts found.

Required:

a) What are the conditions for this experiment to be considered a binomial experiment? Motivate.

b) What is the probability that all parts selected will be defective?

c) What is the probability that none of the parts selected will be defective?

d) What is the probability that more than five parts will be defective?

e) What is the probability that at least three parts will be non-defective?

QUESTION 2

A car dealer has established that 40% of his potential customers prefer single cab cars while 60% prefer double cab cars. From a recent survey among his existing clients, he obtained additional information which indicates that 15% of clients who bought single cab cars prefer air conditioning while 65% of clients who bought double cars prefer air conditioning.

Required:

a) What is the probability that a client who bought a single cab does not prefer air conditioning?

b) What is the probability that a client prefers a double cab with air conditioning?