Question

Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free. You know that the wait times for customers are normally distributed with a mean of 18 minutes and a standard deviation of 3.4 minutes. Use statistics to decide the maximum wait time you would advertise to customers so that you only give away free meals to at most 1.5% of the customers.

a. Determine an estimate of an advertised maximum wait time so that 1.5% of the customers would receive a free meal. Round to one decimal place.

b. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 1.5% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below.

c. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:

-An advanced explanation of the normal distribution

-Why the normal distribution might apply to this situation

-Describe the specific normal distribution for this situation (give the mean and standard deviation)

-Explain how the graph created in part b. represents the waiting times of the customers.

-Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a "nice" wait time to be used in the actual advertising campaign.

-Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.

Answer 1