The Cincinnati Enquirer, in its Sunday business supplement, reported that the mean number of hours worked per week by those employed full time is 43.9. The article further indicated that about one-third of those employed full-time work less than 40 hours

a. Since we know that the mean number of hours worked per week is 43.9, we need to find the standard deviation of the normal distribution. We also know that one-third of those employed full-time work less than 40 hours per week, so we can assume that \approx imately two-thirds work more than 40 hours per week. Using this information, we can estimate that the standard deviation is around 10-12 hours. b. Here, we know that 20% of those working full-time work more than 49 hours per week. Using a standard normal distribution table, we can find the z-score associated with the 20th percentile. The z-score turns out to be 0.84. Then, using the formula z = (x - mu) / sigma, where x is the number of hours worked, mu is the mean (43.9) and sigma is the standard deviation, we can solve for sigma. 0.84 = (49 - 43.9) / sigma Sigma = (49 - 43.9) / 0.84 Sigma ? 6.02 hours The two estimates of the standard deviation are not exactly the same, but they are similar. One possible reason for this is that the distribution of hours worked is not perfectly normal and has some variability. However, both estimates provide a rough idea of how much variability there is in the number of hours worked among those employed full-time. We can conclude that the standard deviation is relatively high, indicating that there is quite a bit of variation in the number of hours worked per week among full-time employees.