Repeat Problem 8, assuming that the number of hours worked by female marketing and advertising managers is normally distributed.
In problem 8
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 full-time men and full-time women in 87 different occupations. According to the article, the mean number of hours (actually) worked by female marketing and advertising managers is μ = 45 hours. Assuming a standard deviation of σ = 7 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 female marketing and advertising managers, chances are roughly 95.44% that the sample mean number of hours worked will be between 31 hours and 59 hours.
b. 95.44% of all possible observations of the number of hours worked by female marketing and advertising managers lie between 31 hours and 59 hours.
c. For a random sample of 196 female marketing and advertising managers, chances are roughly 95.44% that the sample mean number of hours worked will be between 44 hours and 46 hours.