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 16 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 0.5% of the customers.

a. Determine an estimate of an advertised maximum wait time so that 0.5% of the customers would receive a free meal. Round to one decimal place.  minutes

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 0.5% 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. Choose FileNo file chosen

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

1. An advanced explanation of the normal distribution
2. Why the normal distribution might apply to this situation
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. Explain how the graph created in part b. represents the waiting times of the customers.
5. 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.
6. 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

Let X denote the wating times for customer