45. Coffee and doughnuts. At a certain coffee shop,all the

Chapter 16, Problem 45

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45. Coffee and doughnuts. At a certain coffee shop,all the customers buy a cup of coffee; some also buy adoughnut. The shop owner believes that the numberof cups he sells each day is normally distributed with amean of 320 cups and a standard deviation of 20 cups. Healso believes that the number of doughnuts he sells eachday is independent of the coffee sales and is normallydistributed with a mean of 150 doughnuts and a standarddeviation of 12.a) The shop is open every day but Sunday. Assumingday-to-day sales are independent, whats the probabilityhell sell over 2000 cups of coffee in a week?b) If he makes a profit of 50 cents on each cup of coffeeand 40 cents on each doughnut, can he reasonably expectto have a days profit of over $300? Explain.c) Whats the probability that on any given day hell sella doughnut to more than half of his coffee customers?