(3) During your summer internship at a candy company, you are responsible for quality control on the foil-wrapping machine used to cover a certain type of chocolate. The ma- chine individually wraps each chocolate in a piece of foil, and seals 25 wrapped chocolates into a box for sale. According to the manufacturer of the machine, the machine should successfully wrap any given chocolate with probability 0.95, independent of past perfor- mance. Your job is to go through five randomly selected boxes of chocolates, and count the number of defective chocolates in each box. (a) If the manufacturer is correct, explain why the number of defective chocolates in each box can be modeled with a Binomial random variable. (b) If the manufacturer is correct, what is the expected number of defective chocolates in any given box. (c) If the manufacturer is correct, what is the probability of finding 3 defective choco- lates or fewer in any given box. (d) If the manufacturer is correct, what is the probability that all five boxes have more than 3 defective chocolates. (e) What does the Central Limit Theorem say about 7, the sampling distribution of number of defective chocolates per box for a sample of five boxes. the average (f) If the manufacturer is correct, use CLT to approximate the probability that z is greater than 3. (g) If all five boxes had more than 3 defective chocolates, would you still believe the manufacturers claim?