Question: At the end of the first quarter of 2006, a stock market indexes had posted strong gains in the past 12 months. Mass Mutual Financial Group credited the increases to solid growth in corporate profits. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was approximately 12%. The mean one-year return for companies in the Russell 2000, a group of 2000 small companies, was approximately 26%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20% and the standard deviation in the Russell 2000 is approximately 35%.

(a) What is the probability that a stock in the S&P 500 gained 25% or more in the last year? gained 50% or more?

(b) What is the probability that a stock in the S&P 500 lost money in the last year? Lost 25% or more? lost 50% or more?

(c) Repeat (a) and (b) for a stock in the Russell 2000.

(d) Write a short summary on your findings. Re sure to include a discussion of the risks associated with a large standard deviation.