The operations manager of a toll booth located at a major exit of a state turnpike is trying to estimate the average number of vehicles that arrive at the toll booth during a 1-minute period during the peak of rush-hour traffic. In an effort to estimate this average throughput value, he records the number of vehicles that arrive at the toll booth over a 1-minute interval commencing at the same time for each of many normal weekdays. The data are provided in the file P2-9. XLS. 

a. What sample size would be required for the operations manager to be approximately 95% sure that his estimate of the average throughput value is within 1 unit of the true mean? Assume that his best estimate of the population standard deviation σ is 1.7 arrivals per minute. 

b. How does the answer to part a change if the operations manager wants his estimate to be within 0.75 unit of the actual population mean? Explain the difference in your answers to parts a and b.