Question

A certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean μ = 1.8% and standard deviation σ = 0.5%. The fund has over 225 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 225 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable is a mean of a sample size n = 225. By the , the distribution is approximately normal. (

Answer 1

The overall monthly return x for the fund, which is an average return computed using all 225 stocks, has an approximately normal distribution according to the Central Limit Theorem.

Step-by-step explanation:

The overall monthly return x for the mutual fund, which invests in both U.S. and foreign markets, can be considered as an average return computed using all 225 stocks in the fund. Since x is the mean of a sample size n = 225, according to the Central Limit Theorem, the distribution of x will be approximately normal. This theorem states that as the sample size increases, the distribution of the sample mean approaches a normal distribution.

Therefore, because the overall monthly return x is calculated using a large number of stocks (225) in the fund, it follows that x has an approximately normal distribution.