# 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 single randomly selected value is greater than 69.7. P(X > 69.7) =? Write your answers as numbers accurate to 4 decimal places.

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 single randomly selected value is greater than 69.7.
$P\left(X>69.7\right)=$?
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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
The probability that a single randomly selected value is greater than 69.7.
$P\left(X>69.7\right)$
$=P\left(Z>\frac{69.7-73.1}{28.1}\right)$
$=P\left(Z\succ 0.120996441281\right)=0.5482$