Question

Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%

Answer 1

26%

Step-by-step explanation:

Given that Mean, μ = 8.7% = 0.087

Standard Deviation, σ = 20.2% = 0.202

Normal distribution, n = 40

Notice that the distribution annual returns of stocks are a bell-shaped distribution.

hence, using the formula

Zscore = (x - μ ) / σ

= where we have P(return greater than 10%)

= P(x > 0.10)

= P(x > 0.10) = P [z > (0.10 - 0.087)/0.202]

= P (z > 0.0643)

= 1 - P (z > 0.0643)

= Using the value from standard normal z table,

= P (x > 610) = 1 - 0.740 =0.26 = 26%

Hence, the correct answer is 26%.