The price-eamings ratios for all companies whose shares are traded on the New York Stock Exchange follow a normal distribution with standard deviation 3.8. A random sam-

ple of these companies is selected in order to estimate the population mean price-camnings ratio.

(a) How large a sample is necessary in order to ensure that the probability that the sample mean differs from the population mean by more than 1.0 is less than .10?

(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 1.0 is less than .05.

(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 is less than 10.1