Question

find the indicated probability and interpret the result.
from 1975 through 2020, the mean annual gain of the dow jones industrial average was 653. a random sample of 33 years is selected from this population. what is the probability that the mean gain for the sample was between 400 and 700? assume \\( \sigma = 1541 \\).
the probability is 0.3967.
(round to four decimal places as needed.)
interpret the result. select the correct choice and fill in the answer box to complete your choice.
(round to two decimal places as needed.)
o a. about \\( \\% \\) of samples of 33 years will have an annual mean gain between 400 and 700.
o b. about \\( \\% \\) of samples of 46 years will have an annual mean gain between 400 and 700.
o c. about \\( \\% \\) of samples of 33 years will have an annual mean gain between 400 and 653.
o d. about \\( \\% \\) of samples of 33 years will have an annual mean gain between 653 and 700.

Explanation:

Step1: Convert probability to percentage

The probability value \(0.3967\) is converted to a percentage by multiplying by \(100\).

$$0.3967\times100 = 39.67$$

Step2: Match with the options

The sample size in the problem is \(n = 33\) years and the probability is for the mean gain between \(400\) and \(700\).

Answer:

A. About \(39.67\%\) of samples of 33 years will have an annual mean gain between 400 and 700.