The major stock market indexes had strong results in 2018. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was -6.24% The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was -3.88% 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 2018? 

b. What is the probability that a stock in the S&P 500 gained 10% or more in 2018? 

c. What is the probability that a stock in the S&P 500 lost 20% or more in 2018? 

d. What is the probability that a stock in the S&P 500 lost 30% or more in 2018? 

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.