The price-earnings ratios for all companies whose shares are traded on the Tokyo Stock Exchange follow a normal distribution with a standard deviation of 3.5. A random sample of these companies is selected in order to estimate the population mean price-earnings 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 0.8 is less than 0.05?
b. Without doing the calculations, state whether a larger or smaller sample size compared to the sample size in part (a) would be required to guarantee that the probability of the sample mean differing from the population mean by more than 0.8 is less than 0.10.
c. Without doing the calculations, state whether a larger or smaller sample size compared to the sample size in part a would be required to guarantee that the probability of the sample mean differing from the population mean by more than 0.4 hours is less than 0.05.