A hamburger stand sells hamburgers for \$1.45 each. Daily sales have a distribution with a mean of 530 and a standard deviation of 69.

2. A hamburger stand sells hamburgers for \$1.45 each. Daily sales have a distribution with a mean of

530 and a standard deviation of 69.

(a) Find the mean daily total revenues from the sale of hamburgers.

(b) Find the standard deviation of total revenues from the sale of hamburgers.

(c) Daily costs (in dollars) are given by

C = 100 + 0.95X

Where X is the number of hamburgers sold. Find the mean and standard deviation of daily profits from

sales.

(d) (4 points) A manager wonders if the distribution of profits has changed. She samples 20 of these

hamburger stores and finds that the average daily profit is 175 and the sample standard deviation is 25.

Test the hypothesis that average daily profit is still equal to \$165 at α=5% against the alternative that

profit is now greater than \$165. What is your conclusion?

(e) Calculate the approximate p-value from your hypothesis test in (c).