The General Crunch Co. produces and distributes whole grain cereals. Boxes are labeled 16 ounces. Because the amount of cereal in a box is distributed continuously and normally, if the machine that fills boxes is set at 16 ounces, half of all boxes will be underweight, which will anger customers and increase the company's legal expenses. Based on millions of boxes of cereal, the plant manager, Bob Sacamano, has determined the standard deviation of the amount of cereal in all boxes equals 0.2 ounces. (SHOW WORK) a) If Bob Sacamano sets the filling machine to put a mean of 16.3 ounces of cereal in all boxes, what proportion of all boxes will be underweight (meaning, contain less than 16 ounces)? b) [Given Part a] If a customer purchases two boxes of the company's cereal at random, what is the probability at least one of the boxes will be underweight? (HINT: think of 'at least one' as the Union Probability.) c) The company's lead attorney advises the proportion in Part a) is "too high." If the attorney recommends the proportion equal 0.04, what mean setting should Bob Sacamano use? d) The company CEO Susan Ross has "suggested" the filling machine be set at 16.2 ounces to achieve the target proportion of 0.04 (she believes giving cereal away can be as costly as lawsuits). The only way to meet the CEO's suggestion is to reduce the standard deviation. What standard deviation must Bob Sacamano achieve? e) [Given Part d) results for and ] Because the CEO is concerned about giving cereal away, she asks Bob Sacamano to determine the proportion of all boxes that will contain more than 16.3 ounces of cereal. Determine the proportion. f) [Given Parts d and e] If the company produces 1,500,000 boxes of cereal in the next year, how many boxes do you expect to contain more than 16.3 ounces of cereal? g) [Given Part d] Ninety-seven and one-half [97.5] percent of all boxes of cereal produced will contain at least how much cereal?