# A population of values has a normal distribution with \mu=73.1 and \sigma=28.1. You intend to draw a random sample of size n=131. Find the probability

A population of values has a normal distribution with $\mu =73.1$ and $\sigma =28.1$. You intend to draw a random sample of size $n=131$.
Find the probability that a sample of size $n=131$ is randomly selected with a mean greater than 69.7.
$P\left(M>69.7\right)=$?
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joshyoung05M
Step 1
Let us denote X= population values
Given that X follows a normal distribution with mean $=\mu =73.1$ and standard deviation $=\sigma =28.1$
Step 2
n=sample size = 131
So, $M=\stackrel{―}{X}$ follows a normal distribution with mean $=\mu =73.1$ and standard deviation $=\frac{\sigma }{\sqrt{n}}=\frac{28.1}{\sqrt{131}}=2.45510839922$
the probability that a sample of size $n=131$ is randomly selected with a mean greater than 69.7.
$P\left(M>69.7\right)$
$=P\left(Z>\frac{69.7-73.1}{2.45510839922}\right)=0.9170$