The major stock market indexes had strong results in 2017. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was +10.42%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was +28.74%. 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 2017?

b. What is the probability that a stock in the S&P 500 gained 10% or more in 2017?

c. What is the probability that a stock in the S&P 500 lost 20% or more in 2017?

d. What is the probability that a stock in the S&P 500 lost 30% or more in 2017?

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.