The number of hours spent studying by students on a large campus in the week before final exams follows a normal distribution with standard deviation 8.4 hours. A random sample of these students is taken to estimate the population mean number of hours studying.

(a) How large a sample is needed to ensure that the probability that the sample mean dif- fers from the population mean by more than 2.0 hours is less than .05?

(b) Without doing the calculations, state whether a larger or smaller sample than that in part

(a) would be required to guarantee that the probability that the sample mean dif- fers from the population mean by more than 2.0 hours is less than 10.

(c) Without doing the calculations, state whether a larger or smaller sample than that in part

(a) would be required to guarantee that the probability that the sample mean dif- fers from the population mean by more than 1.5 hours is less than .05.