Question

The rate of return of stock indexes is approximately normal. Since 1945, the Standard & Poor's 500 has had a mean return of about 12%, with a standard deviation of about 16.5%. Take this normal distribution to be the distribution of yearly returns over a long period. a) In what range do the middle 95% of all yearly returns lie? b) The market is down for the year if the return on the index is less than zero. In what percent of years is the market down?

Name: the rate of return of stock indexes is approximately normal since 1945 the standard poors 500 has had a mean return of about 12 with a standard deviation of about 165 take this normal distri 43786
Uploaded: 2023-12-11T20:52:20-08:00
Duration: 2 min 2 s
Channel: Tim Thornhill
Description: the rate of return of stock indexes is approximately normal since 1945 the standard poors 500 has had a mean return of about 12 with a standard deviation of about 165 take this normal distri 43786

          The rate of return of stock indexes is approximately normal.
Since 1945, the Standard
& Poor's 500 has had a mean return of about 12%, with a
standard deviation of about
16.5%. Take this normal distribution to be the distribution of
yearly returns over a long
period.
a) In what range do the middle 95% of all yearly returns lie?
b) The market is down for the year if the return on the index is
less than zero. In
what percent of years is the market down?

Added by Jennifer S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Tim Thornhill

12/11/2023

Step 1

The mean (\(\mu\)) is 12%, and the standard deviation (\(\sigma\)) is 16.5%. Show more…

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The rate of return of stock indexes is approximately normal. Since 1945, the Standard & Poor's 500 has had a mean return of about 12%, with a standard deviation of about 16.5%. Take this normal distribution to be the distribution of yearly returns over a long period. a) In what range do the middle 95% of all yearly returns lie? b) The market is down for the year if the return on the index is less than zero. In what percent of years is the market down?