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# Statistics - Probability

4. In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. Martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. Suppose we randomly select a sample of 100 blue-collar workers. Based on Martocchio's estimates, find, by hand:

a. What is the probability that the average amount of paid time lost during a threeâ?month period for the 100 blue-collar workers will exceed 1.5 days?

b. What is the probability that the average amount of unpaid time lost during a three-month period for the I00 blue-collar workers will exceed 1.5 days?

c. For the amount of paid time lost, the probability is 60% that the sample mean will be between what two values, symmetrically distributed around the population mean?

Note- Use a 0.05 level of significance where needed.