At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. the shop owner believes that the number of cups he sells each day is normally distributed with a mean of 360 cups and a standard deviation of 21 cups. he also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 180 doughnuts and a standard deviation of 17. complete parts a) through c).
a) the shop is open every day but sunday. assuming day-to-day sales are independent, what’s the probability he’ll sell over 2000 cups of coffee in a week?
b) if he makes a profit of 50 cents on each cup of coffee and 40 cents on each doughnut, can he reasonably expect to have a day’s profit of over $300? explain.
c) what’s the probability that on any given day he’ll sell a doughnut to more than half of his coffee customers?