Question: Many Happy Returns is a tax preparation service with offices located throughout the western United States. Suppose the average number of returns processed by employees of Many Happy Returns during tax season is 12 per day with a standard deviation of 3 per day. A random sample of 36 employees taken during tax season revealed the following number of returns processed daily:
a. What is the probability of having a sample mean equal to or smaller than the sample mean for this sample if the population mean is 12 processed returns daily with a standard deviation of 3 returns per day?
b. What is the probability of having a sample mean larger than the one obtained from this sample if the population mean is 12 processed returns daily with a standard deviation of 3 returns per day?
c. Explain how it is possible to answer parts a and b when the population distribution of daily tax returns at Many Happy Returns is not known.