Question

Andrew plans to retire in 32 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. (a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 32 years will exceed 10%? (b) What is the probability that the mean return will be less than 4%?

(a)

(b)

please take me to step by step how you came to your solution. Thank you

Answer 1

This is a normal distribution question with

a)

P(x > 10.0)=?

The z-score at x = 10.0 is,

z = 0.0644

This implies that

P(x > 10.0) = P(z > 0.0644) = 1 - 0.5256741349857433

b)

P(x < 4.0)=?

The z-score at x = 4.0 is,

z = -0.2327

This implies that

PS: you have to refer z score table to find the final probabilities.

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