Answered: Coffee and doughnuts At a certain…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Coffee and doughnuts At a certain coffee shop, all the

customers buy a cup of coffee; some also buy a dough-
nut. 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 20 cups. He also
believes that the number of doughnuts he sells each day

is independent of the coffee sales and is normally distrib-
uted with a mean of 150 doughnuts and a standard devia-
tion of 12.

a) The shop is open every day but Sunday. Assuming

day-to-day sales are independent, what’s the probabil-
ity he’ll sell over 2000 cups of coffee in a week?

b) If he makes a profit of 50 cents on each cup of cof-
fee 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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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