Question

# At a certain coffee​ shop, all the customers buy a cup of coffee and some also...

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 310 cups and a standard deviation of 22 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 15. 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.

A. No.​ \$300 is more than 5 standard deviations above the mean.

B. No. The number of doughnuts he expects to sell plus the number of cups of coffee is less than 600.

C. Yes.​ \$300 is less than 6 standard deviations above the mean.

D. Yes. The number of doughnuts he expects to sell plus the number of cups of coffee is greater than 300.

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

So, everything beyond 2 deviation is unusual.

Lets see how much is the expected value at 2 deviation above mean

For coffee, expected mean of the combined distribution = Mean 1 + Mean 2 = .5*310 + .4*180 = \$227

For donut, expected mean of the combined distribution = sqrt((.5*22)^2 + (.4*15)^2) = \$12.53

So, \$300 is (300-227)/12.53 = 5.83 deviations away from mean

So, A is correct. It is unusual to expect \$300

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