Pick any positive values for the mean and the standard deviation of a normal distribution. Use your selection of a normal distribution to answer the questions below. The results of parts (a) to (c) form what is often called the Empirical Rule for the standard deviation in a normal distribution.
(a) Verify that about 95% of the values fall within two standard deviations of the mean.
(b) What proportion of values fall within one standard deviation of the mean?
(c) What proportion of values fall within three standard deviations of the mean?
(d) Will the answers to (b) and (c) be the same for any normal distribution? Explain why or why not.