Question 6 (Show step by step calculation in Excel or explain your Excel function. Round the answer in 4 decimal places if possible)

A car manufactory has a probability of 0.04 to produce a lemon. Suppose this probability is independent of the others.

A lemon means a car has problem that need to be fixed. Lemon cannot be sent to dealership.

100 cars were manufactured from this manufactory.

Question 6

a. use the Poisson process to approximate the this question. What is the mean and variance of this Poisson approximation?

Mean of this Poisson approximation:

Variance of this Poisson approximation:

b. under the Poisson approxmation, what is the probability that all cars are good to send to dealership?

c. Under the Poisson approximation, what is the probability at most four cars are lemon?

d) What is the variance of the number of lemon?