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Question

From 1975 through 2020 the main annual gain of the Dow Jones industrial average was 652 a random sample of 35 years is selected from this population. What is the probability that the main gain for the sample was between 500, and 8 hundred assume standard deviation of 1540.

Answer 1

mu= population mean = 652

small sigma =1540 = population standard deviation

s= sigma/sqrN= 1540/sqr35= about 260.31 = sample standard deviation

find probability that sample mean is between 500 and 800,

find the z scores, for 5 and 8 hundred

-152/260=about -.584 = z for 500

148/260= about .569 = z for 800

now find corresponding areas under the normal curve from 0 to z, and add them

use z tables or a z calculator

.220 + .215 = .435= 43.5 % chance sample mean is between 5 and 8 hundred