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Q.12

Expert-verifiedFound in: Page 428

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

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

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

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

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

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

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

$\mathrm{P}(X\le 7000)=0.0569$94% of StudySmarter users get better grades.

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