The S&P 500 is a collection of 500 stocks of publicly traded companies. Using data obtained from

Question:

The S&P 500 is a collection of 500 stocks of publicly traded companies. Using data obtained from Yahoo! Finance, the monthly rates of return of the S&P 500 since 1950 are normally distributed. The mean rate of return is 0.007233 (0.7233%), and the standard deviation for rate of return is 0.04135 (4.135%).

(a) What is the probability that a randomly selected month has a positive rate of return? That is, what is P(x > 0)?

(b) Treating the next 12 months as a simple random sample, what is the probability that the mean monthly rate of return will be positive? That is, with n = 12, what is P(x̄ > 0)?

(c) Treating the next 24 months as a simple random sample, what is the probability that the mean monthly rate of return will be positive?

(d) Treating the next 36 months as a simple random sample, what is the probability that the mean monthly rate of return will be positive?

(e) Use the results of parts (b)–(d) to describe the likelihood of earning a positive rate of return on stocks as the investment time horizon increases.

Stocks
Stocks or shares are generally equity instruments that provide the largest source of raising funds in any public or private listed company's. The instruments are issued on a stock exchange from where a large number of general public who are willing...