The Cincinnati Enquirer, in its Sunday business supplement, reported that full-time employees in the region work an average of 43.9 hours per week. The article further indicated that about one-third of those employed full time work less than 40 hours per

a. To find the standard deviation of the number of hours worked, we need to know the mean and the percentage of people working less than 40 hours per week. We know that the mean is 43.9 hours per week. If one-third of people work less than 40 hours per week, that means two-thirds work more than 40 hours per week. Using this information, we can estimate the standard deviation using the empirical rule, which states that for a normal distribution, \approx imately 68% of values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. Therefore, if two-thirds of the workers work more than 40 hours per week, \approx imately 34% work between 40 and 43.9 hours per week, so about 17% work between 40 and 43.9 hours per week on either side of the mean. Using the empirical rule, we can estimate that one standard deviation is \approx imately (43.9-40)/1.67 = 2.10 hours. Therefore, the standard deviation of the number of hours worked is \approx imately 2.10 hours. b. To determine the standard deviation with the information that 20% of those working full time work more than 49 hours per week, we can use the same approach as in part a. We know that 20% of the workers work more than 49 hours per week, so \approx imately 80% work less than 49 hours per week. Using the empirical rule, we can estimate that \approx imately 40% work between 43.9 and 49 hours per week, which means \approx imately 20% work between 43.9 and 46.5 hours per week on either side of the mean. Using the same formula as in part a, we can estimate that one standard deviation is \approx imately (49-43.9)/1.67 = 3.07 hours. Therefore, the standard deviation of the number of hours worked for workers who work more than 49 hours per week is \approx imately 3.07 hours. The estimates of the standard deviation in parts a and b are not similar, with an estimate of 2.10 hours in part a and an estimate of 3.07 hours in part b. This is because the two scenarios have different distributions of hours worked. In part a, we assumed that two-thirds of workers work more than 40 hours per week and roughly evenly distributed around the mean. In part b, we assumed that 20% of workers work more than 49 hours per week and the distribution is skewed towards the higher end. Therefore, the estimate of the standard deviation is higher because there are more extreme values in the distribution.