# 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.

(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.

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