1. Ball bearings are manufactured with a mean diameter of 5 millimeters (mm).Because of variability in the manufacturing process,the diameters of the ball bearings are known to be approximately normally distributed with a standard deviation of 0.023 mm.

a)What proportion of the ball bearings have a diameter between 4.95 mm and 5.05 mm?Interpret the meaning of your answer.(12 points)

b)Any ball bearings that have a diameter less than 4.95 mm or more than 5.05 mm are discarded. If 30,000 ball bearings are manufactured in a day, how many can the plant manager expect to discard?(12 points)

3.The mean gas mileage for a particular hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 5.5 miles per gallon.

a)What is the probability a randomly selected hybrid car will get under 62 miles per gallon? (10 points)

b)Determine the gasoline mileage, in miles per gallons, that make up the middle 85% of mileages for this hybrid car.(12 points)

4.Scores for a civil service exam are normally distributed, with a standard deviation of 7.To be eligible for civil service employment, you must score in the top 5%.If the lowest score you can earn and still be eligible for employment is an 85, what is the mean score for the exam? (10 points)