Describe the normal distribution including the function that represents it, the value expected and standard deviation. Present two examples. A. A machine that produces bearings was programmed so that the diameter of the part outside .500 inches. A bearing is acceptable if its diameter it is .004 inches from this value. Suppose the schedule was changed during the course of production so that the diameter of bearings is normally distributed averaging .499 inches and a standard deviation of .002 inches, what percent of the bearings produced would not be acceptable? b. Studies have shown that the mileage (mpg) of gasoline in compact cars in the U.S. is normally distributed with a mean of 25.5 miles per gallon and a standard deviation of 4.5 mpg. i. What percent of compact cars perform greater than 30 mpg. ii. If a manufacturer wants to develop a compact car that has a performance greater than 95% of current compacts, which must be the gas mileage for this new car? c. A manufacturing plant uses 3,000 electric bulbs that have a duration that is normally distributed with an average of 500 hours and a 50-hour standard deviation. To minimize the number of bulbs that burn out during operating hours, bulbs should be replaced after a certain period of operation. How often do bulbs need to be replaced if we want at most one per one hundred (1%) of the bulbs burn out between replacement periods?