For many years the MBA Club at Piedmont Business School has held its Friday afternoon beer blasts at She's Not Here, a local watering hole with a nautical ambiance, run by a retired admiral, Andy Bunch.In the past, the MBA's had always consumed whatever beer Andy had on draught, and Andy always had enough beer available to meet demand.Andy kept careful records, and after examining them decided that the MBA's Friday afternoon beer consumption was normally distributed with mean 40M oz. and standard deviation 10M oz., where M was the number of MBA's drinking that afternoon.

a)Suppose 40 students stop by on a given Friday.

What is the probability that their beer consumption is

i) less than 2200 oz.?

ii)between 1200 and 2000 oz.?

iii)(5 pts) more than 2100 oz.?

Following the success if its low calorie "Life" beer, the Mueller Brewing Company has developed specialty beers aimed at specific market segments.The advertising campaign supporting "MBA Brew" ("The Beer on the Fast Track") has been so successful that this year the MBA's at She's Not Here drink nothing but "MBA Brew."Andy believes that their demand for "MBA Brew" is the same as their historic demand for whatever he had on tap.However, nobody besides MBA's will drink "MBA Brew," so Andy is unwilling to stock enough of it to guarantee that all demand will be met.

b)Suppose that Andy stocks 25 gallons (3200 oz.).If 65 students drop by, what is the probability that Andy will run out of "MBA Brew"?

c)On an ordinary Friday afternoon, between 25 and 55 MBA's stop by.However, after the QM exam today, Andy estimates there will be 70 MBA's in to drown their sorrows.

i) How much MBA brew should he stock to be 98% certain that he will be able to meet demand?

ii)(8 pts) If he stocks this amount, and 90 MBA's actually stop in, what is the probability that he will run out?

d)Suppose Andy stocks 50 gallons (6400 oz.).What is the greatest number of MBA's for which Andy can be 95% certain that he won't run out?