4.20 The data below represent earnings (in dollars) for a random sample of five common stocks listed on the New York Stock Exchange.

1.68, 3.35, 2.50, 6.23, 3.24

(a) Use the most appropriate test to see if these data can be regarded as a random sample from a normal distribution.

(b) Use the most appropriate test to see if these data can be regarded as a random sample from a normal distribution with m ¼ 3, s ¼ 1.

(c) Determine the sample size required to use the empirical distribution function to estimate the unknown cumulative distribution function with 95% confidence such that the error in the estimate is (1) less than 0.25 and (2) less than 0.20.