Hours Actually Worked. In the article “How Hours of Work Affect Occupational Earnings” (Monthly Labor Review, Vol. 121), D. Hecker discussed the number of hours actually worked as opposed to the number of hours paid for. The study examines both men and women in 87 different full-time occupations. According to the article, the mean number of hours (actual) per week worked by men employed in firefighting is μ = 51 hours. Assuming a standard deviation of σ = 5 hours, decide whether each of the following statements is true or false or whether the information is insufficient to decide. Give a reason for each of your answers.

a. For a random sample of 196 male in firefighting occupation, chances are roughly 95% that the sample mean number of hours worked will be between 45 hours and 55 hours.

b. Approximately 95% of all possible observations of the number of hours worked by male in firefighting occupation lie between 45 hours and 55 hours.

c. For a random sample of 196 male in firefighting occupation, chances are roughly 95% that the sample mean number of hours worked will be between 50 hours and 53 hours.