Information for Questions 24 - 25: 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 from 1950 through 2010 are normally distributed. The mean rate of return is 0.007443 and the standard deviation is 0.04135.
24. What is the probability that a randomly selected month has a positive rate of return? That is, what is P(X > 0)?
a. 0.57
b. 0.43
c. 0.36
d. 0.50
e. 0.68
25. What is the probability that the mean monthly return for a one year period is positive? That is, for n = 12 months, what is P(X̄ > 0)?
a. 0.57
b. 0.43
c. 0.27
d. 0.73
e. 0.50