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The major stock market indexes had strong results in 2016. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was +9.54%. The mean one-year return for Chapter Review Problems 245 246 CHAPTER 6 | The Normal Distribution and Other Continuous Distributions the NASDAQ, a group of 3,200 small and medium-sized companies, was +7.50%. 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 2016?

b. What is the probability that a stock in the S&P 500 gained 10% or more in 2016?

c. What is the probability that a stock in the S&P 500 lost 20% or more in 2016?

d. What is the probability that a stock in the S&P 500 lost 30% or more in 2016?

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.