The quality-control manager of a long john silver's restaurant wants to analyze the length of time that a car spends at the drive-through window waiting for an order. 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. 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? treat the next 50 cars that arrive as a simple random sample. there is 15% chance the meantime will be at or below seconds?