From past data it is known that the distribution of annual returns on common sto

Question

From past data it is known that the distribution of annual returns on common stocks has an expected value µ equal to 7% and a standard deviation s of 20%. However, the distribution of annual returns is skewed and therefore cannot be described by a normal model. Sheila plans to retire in 32 years and is considering investing in stocks.
Question 1. What is the probability (assuming that past patterns of annual returns continue) that the mean annual return x on common stocks over the next 32 years will exceed 8%?
(use 4 decimal places in your answer)
Question 2. What is the probability (assuming that past patterns of annual returns continue) that the mean annual return x on common stocks over the next 32 years will be less than 3%?
(use 4 decimal places in your answer)
Question 3. The Central Limit theorem was needed to answer questions 1 and 2 above.
True
False

Explanation / Answer

Given µ= 0.07 and standard deviation s = 0.2
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Question 1. What is the probability (assuming that past patterns of annual returns continue) that the mean annual return x on common stocks over the next 32 years will exceed 8%?
(use 4 decimal places in your answer)

P(xbar > 0.08) = P((xbar-)/(s/n) > (0.08-0.07)/(0.2/sqrt(32)))

=P(Z> 0.28)

=0.3897 (check standard normal table)

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Question 2. What is the probability (assuming that past patterns of annual returns continue) that the mean annual return x on common stocks over the next 32 years will be less than 3%?
(use 4 decimal places in your answer)

P(xbar < 0.03) = P((xbar-)/(s/n) < (0.03-0.07)/(0.2/sqrt(32)))

=P(Z< -1.13)

=0.1292 (check standard normal table)

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Question 3. The Central Limit theorem was needed to answer questions 1 and 2 above.
True

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