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New York Stock Exchange. Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange follows a non-normal distribution with mean = 15 percent and a standard deviation of = 5 percent.

Find the probability that the mean return for the 40 sampled stocks is between 13.5 and 16 percent. To facilitate a more convenient reporting, we have separated this question into two parts below:

i. Report the z-scores corresponding to 13.5 percent and 16 percent to two decimal places.

ii. Report the final probability to 4 decimal places.

(e) What is the value of the sample mean that corresponds to the 80th percentile for the sampling distribution of the sample mean based on a sample of 40 stocks? Compute this value and report the answer to two decimal places.

(f) Companies are often concerned with the notion of worst probable case performance of their portfolios. They wish to know the mean return such that we would expect 99% of samples of 40 stocks to perform better than this mean return. Compute this value and report the answer to two decimal places.