The major stock market indexes had mixed results in 2011. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was -1.8%. Historically, the one-year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%.
a. What is the probability that a stock in the S&P 500 gained value in 2011?
b. What is the probability that a stock in the S&P 500 gained 10% or more in 2011?
c. What is the probability that a stock in the S&P 500 lost 20% or more in 2011?
d. What is the probability that a stock in the S&P 500 lost 40% or more in 2011?
e. Repeat (a) through (d) for a stock in the NASDAQ.
f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.