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Q.12

Expert-verified
Found in: Page 428

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

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# Find the probability that the sum of the $40$ values is less than $7,000$.

The probability that the sum of the $40$ values is less than $7000$ is $\mathrm{P}\left(X\le 7000\right)=0.0569$.

See the step by step solution

## Step 1: Given Information

A mean (${\mu }_{x}$) is$180$ and a standard deviation $\left(\sigma \right)$ is $20$.

## Step 2: Explanation

To find the probability that the sums of the $40$ values is less than $7000$:

localid="1649346312817" $\sum X~N\left(n{\mu }_{x},\sqrt{n}{\sigma }_{x}\right)$

$\sum X~N\left(\left(40\right)\left(180\right),\left(\sqrt{40}\right)\left(20\right)\right)$

localid="1649346327071" $\mathrm{P}\left(X\le 7000\right)=\mathrm{P}\left(Z\le \frac{X-n{\mu }_{x}}{\sqrt{n}{\sigma }_{x}}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{P}\left(Z\le \frac{7000-7200}{126.4911}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{P}\left(Z\le -1.5811\right)$

$\mathrm{P}\left(X\le 7000\right)=0.0569$

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