The quality-control manager of a Long John Silver’s restaurant wishes to analyze the length of time that a car spends at the drive-through window waiting for an order. According to records obtained from the restaurant, it is determined that the mean time spent at the window is 59.3 seconds with a standard deviation of 13.1 seconds. The distribution of time at the window is skewed right (data based on information provided by Danica Williams, student at Joliet Junior College).

(a) To obtain probabilities regarding a sample mean using the normal model, what size sample is required?

(b) The quality-control manager wishes to use a new delivery system designed to get cars through the drive-through system faster. A random sample of 40 cars results in a sample

mean time spent at the window of 56.8 seconds. What is the probability of obtaining a sample mean of 56.8 seconds or less, assuming that the population mean is 59.3 seconds? Do you think that the new system is effective?

(c) Treat the next 50 cars that arrive as a simple random sample. There is a 15% chance the mean time will be at or below ________ seconds.