At the end of the first quarter of 2006, all the major 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?
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