Question

Andrew plans to retire in 38 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 38 years will exceed 13%? (b) What is the probability that the mean return will be less than 5%?

          Andrew plans to retire in 38 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 38 years will exceed 13%?
(b) What is the probability that the mean return will be less than 5%?

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Andrew plans to retire in 38 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 38 years will exceed 13%?
(b) What is the probability that the mean return will be less than 5%?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

03/22/2022

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Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:06 In the question here, we want to discuss about the normal distribution.

00:13 And let me remind you that if we have the x that followed by the normal with the mean and standard deviation, and then if we turn the x, we minus the mean of the standard deviation, it will follow by the standard normal.

00:29 And now we will have the answer the formula for the x -par minus the mean of a standard division.

00:38 We need to divide by square -up -n and in order to obtain the standard standard normal.

00:44 Now we will have the real annual return common stock x and we will have the normal form with the mean equal to the 8 .7 % and standard division equal to the 20 .2%.

01:05 And the distribution will be the normal.

01:09 And one is the probability that the mean annual return on the common stock over the next 36 -38 years.

01:16 So it means that the end equal to the 38.

01:18 Now the question i asked me to find the probability that the sum of the x bar will be created than the 13%.

01:25 Now to find this probability, we need to confirm the x into the z.

01:30 And to do it, we need to apply the formula for the x -par.

01:34 And we need to turn the 13 minus the mean, divided by the standard deviation over the square of n will be the 38.

01:43 Now when we compute, we have the z -quator then 13 -7, divided by 20 .2 times with the square root than the 38 equals 1 .3 -1.

01:57 Now to find this probability, i need to put it to put it...

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