Question: The monthly profits of outlets of a chain of fast food restaurants are normally distributed with mean 115 and standard deviation 10 (in thousands of dollars). Suppose X denotes the profits of an outlet.

Find the following probabilities (6 points each)

a)

b)

c)

(d) The national headquarters of the chain pays a bonus to those stores whose sales are in the top 5% of franchise sales. What is the minimum sales level required to earn a bonus? (7 points)

(e) Suppose a random sample of 25 stores is selected. What is the probability that the mean sales of this sample will be within 2 standard deviations of the population mean? (7 points)