1. Suppose that you are the manager at a manufacturing plant that produces metal ball bearings. The machines that produce the ball bearings produces ball bearings that follow a normal distribution with an average diameter of 5mm and a standard deviation of 0.02mm. a) (2.5pts) What is the probability of randomly selecting a ball bearing with a diameter which exceeds 5.03mm? b) (2.5pts) A ball bearing is considered faulty and is discarded if its diameter exceeds 5.05mm or falls below 4.95mm. What percentage of ball bearings will be discarded? c) (2pts) How many faulty ball bearings should you expect to find in a batch of 30,000? d) (2pts) Suppose an order comes into your office for exactly 30,000 ball bearings. How many ball bearings do you need to put into production in order fulfill the order? e) (2pts) If a small batch of 100 ball bearings are randomly and independently selected for quality control purposes, what is the probability that only 5 of them will be faulty