A graphing calculator may be used wherever possible. However, you need to substantiate your answers for full credit if necessary. If you are to use a decimal for a probability, round your answer to four decimal places. [1](12) To determine the order in which customers are served, the meat department of a large supermarket utilizes an electronic device that issues a number to each customer waiting to be served. To collect data on customer waiting times, the clerk enters the customer's number in the machine when he or she is served. The store will add additional clerks if it finds that the mean wait time exceeds 90 seconds. A sample of 38 customers reveals an average waiting time of 91.5 seconds. Let's assume that the standard deviation for all customer waiting times is 7.8 seconds. a) Is it reasonable to think that the distribution of customer waiting times is normal in shape? Explain. b) What is the value of the point estimate for the mean waiting time? c) Find the probability that the average waiting time of a sample of 38 customers exceeds 91.5 seconds without additional clerks. d) We wish to construct a 95% confidence interval estimate of the mean waiting time for all customers at the meat department without additional clerks using the given data. What distribution do you apply to estimate for the population mean / to the given situation? e) What is the critical value za/2?f) What is the value of the margin of error E? g) Construct a 95% confidence interval estimate of the mean waiting time for all customers at the meat department without additional clerks. You can do it using the results from (e) and (f) or using TI-84. h) Does the situation constitute sufficient evidence to indicate that additional help is