1. Consider a single-machine production system that produces aluminum sheets for car manufacturing. The monthly production target is 100 sheets. The minimum and maximum thickness of the aluminum sheets should be between 2,97 and 3.03 millimeters to meet the car manufacturing standards. The historical data shows that the thickness of the sheets produced by the current pressing machine has a normal distribution with a mean of 3.00 mm and a standard deviation of 0.02mm. (a) (25 pts) Use the normal approximation to the binomial yield model to estimate the probability that the production requirements are met if the number of items that are manufactured is 100, 110, and 120. (b) (25 pts) Repeat the same exercise if the required quantity is 1000 and 1000, 1100, and 1200 items are produced