In a Study of Radio Listening Habits, a Station Owner $\sigma$

Essay

In a study of radio listening habits, a station owner would like to estimate the average number of hours that teenagers spend listening each day. If it is reasonable to assume that $\sigma$ = 1.3 hours, how large a sample size is needed to be 90% confident that the sample mean is off by, at most, 30 minutes? Justify your conclusion.