# A population of values has a normal distribution with \mu=226.7 and \sigma=59.8. If a random sample size of n=24 is selected. Find the probability that a single randomly selected value is greater than 192.5.

FobelloE 2021-03-02 Answered
A population of values has a normal distribution with $\mu =226.7\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\sigma =59.8$. If a random sample size of n=24 is selected.
Find the probability that a single randomly selected value is greater than 192.5.
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## Expert Answer

Laaibah Pitt
Answered 2021-03-03 Author has 98 answers

Let
The probability that a single randomly selected value is greater than 192.5 is,
$P\left(X>192.5\right)=1-P\left(X\le 192.5\right)$
$=1-P\left(\frac{X-\mu }{\sigma }\le \frac{20-45}{12}\right)$
$=1-P\left(z\le -0.57\right)$
$=1-\left(=NORMDIST\left(-0.57\right)\right)$ (Using the excel fromula)
$=1-0.2843=0.7157$
Therefore, the required probability is, 0.7157.

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