Question

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 320 cups and a standard deviation of 24 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 150 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?

​(Round to three decimal places as​ needed.)

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

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

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

​

c) What's the probability that on any given day​ he'll sell a doughnut to more than half of his coffee​ customers?

​(Round to three decimal places as​ needed.)

Answer 1

fata Given .6 days Hem -320 24 me weer 7 days ; CEPA Spokey eta Gill - 6x320 1920 o no. 56x24 58 59 p(x > 3000): plant, ) - HP[74 303 ] from I table 0.0861 E1-0.9199 P1472000) = 0.0got 6) Daily profit mem - 320 * 50 + 150 vuonna = 1604603 Daily profit mean - 210 + (0.6*17 144 +46 24 at van 105 X24) n . 190.24 Plx>300) = P[22 3.010.30) - P[775,6] 1-P[z 258 from I table more than 5 standard deviation above the mean Plx>300) = 0 No $300 moe Pon 5 St option A is correct la Y-DŹC W 160 - 05*320 - 16 (V) va (0) No (OS) + 029 x 24 4 33 plv20) : P[22 06-10) - P[z> 0181] - 1-P124048] +1 -0.6847 +0.363