The​ price-earnings ratios for all companies whose shares are traded on a specific stock exchange follow a normal distri

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The​ price-earnings ratios for all companies whose shares
are traded on a specific stock exchange follow a normal
distribution with a standard deviation of 3.7. A random sample of
these companies is selected in order to estimate the population
mean​ price-earnings ratio. Complete parts​ (a)
through​ (c).
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 1.1 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
1.1 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
1.6 is less than 0.05.