11.40 Returns on stocks. Andrew plans to retire in 40 years. He is thinking ofin

Question

11.40 Returns on stocks. Andrew plans to retire in 40 years. He is thinking ofinvesting his retirement funds in stocks, so he seeks outinformation on past returns. He learns that over the 101 yearsfrom 1900 to 2000, the real (that is, adjusted forinflation) returns on U.S.common stocks had mean 8.7%and standarddeviation 20.2%. The distribution ofannual returns on common stocks is roughly symmetric, sothe mean returnover even a moderate number of years is close to Normal. Whatis the probability (assumingthat the past pattern of variation continues) thatthe mean annualreturn on common stocks over the next 40 years will exceed10%? What is the probability thatthe mean returnwill be less than 5%?Follow the four-step process inyour answer.

Explanation / Answer

µ = 8.7 s = 20.2 <-- Should be sigma, but the program isn't working z = (x-µ)/s P(x > 10) = P(z > (10 - 8.7)/20.2)    = P(z > 0.06)    = 1 - (z < 0.06) Look up 0.06 on a Table of values    = 1 - 0.5239    = 0.4761 If you don't have a table of values, you can use a program on a Texas Instrument Graphing Calculator P(x < 5) = P(z < (5-8.7)/20.2)    = P(z < 0.18)    = 0.4286

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