# A population of values has a normal distribution with \mu=26.8 and \sigma=33.8. Yo

A population of values has a normal distribution with $\mu =26.8$ and $\sigma =33.8$. You intend to draw a random sample of size $n=89$.
Find the probability that a sample of size $n=89$ is randomly selected with a mean between 17.1 and 25.
$P\left(17.1?

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Step 1
It is given that a population of values distributed normally with mean 26.8 and standard deviation 33.8. The sample size is 89.
Step 2
Calculate the probability that a sample of size $n=89$ is randomly selected with a mean between 17.1 and 25 is as follows:
$P\left(17.1
$=P\left(\frac{17.1-26.8}{\frac{33.8}{\sqrt{89}}}
$P\left(-\frac{9.7}{3.58279}
$=P\left(-2.707

$=0.3078-0.0034=0.3044$
Therefore, the value of $P\left(17.1.