# Sample Distribution - New York Stock Exchange

This question has to deal with the sampling distribution of the sample mean.

Please see attached file for full problem description.

Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4% and a standard deviation of 20.6%. Consider drawing a random sample of n=5 stocks from the population of all stocks and calculating the mean return, x, of the sampled stocks. Find the mean and the standard deviation of the sampling distribution of x, and find an interval containing 95.44% of all possible sample mean returns.

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#### Solution Summary

Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4% and a standard deviation of 20.6%. Consider drawing a random sample of n=5 stocks from the population of all stocks and calculating the mean return, x, of the sampled stocks. Find the mean and the standard deviation of the sampling distribution of x, and find an interval containing 95.44% of all possible sample mean returns.

Z values

The daily trading volumes (millions of shares) for stocks traded on the New York Stock Exchange for twelve days in a certain period are given below. See attachment.

Assume that the probability distribution of trading volumes is approximately normal.

1. Compute mean and standard deviation for daily trading volumes to use as estimates of the population mean and standard deviation.

2. What is the probability that on a particular day the trading volume will be less than 800 million shares?

3. What is the probability that on a particular day the trading volume will exceed 1 billion shares?

4. If the exchange wants to issue a press release on the top 5% of trading days, what volume will trigger a press release?