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Suppose the average number of returns processed by employees of a tax preparation service during tax season is 12 per day with a standard deviation of 6 per day. A random sample of 36 employees taken during tax season revealed the number of returns processed daily shown below. Use these data to answer parts a through c.
13 12 17 12 8 14 9 16 13 17 14 13 11 8 20 15 13 12 9 9 8 16 17 9 10 12 13 11 9 18 3 3 27 8 10 21
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 6 returns per? day?
b. What is the probability of having a sample mean larger than the sample mean for this sample if the population mean is 12 processed returns daily with a standard deviation of 6 returns per? day?
Answers must be rounded up to four decimal places.
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