A population of values has a normal distribution with \mu=182.5 and \sigma=49.4. You intend to draw a random sample of size n=15. Find the probability that a single randomly selected value is greater than 169.7. P(X > 169.7) =? Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with $\mu =182.5$ and $\sigma =49.4$. You intend to draw a random sample of size $n=15$.
Find the probability that a single randomly selected value is greater than 169.7.
$P\left(X>169.7\right)=$?
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Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with mean $\mu =182.5$ and a standard deviation $\sigma =49.4$. The sample size is 15.
Step 2
The probability that a single randomly selected value is greater than 169.7 is
$P\left(X>169.7\right)=P\left(\frac{X-\mu }{\sigma }>\frac{169.7-182.5}{49.4}\right)$
$=P\left(Z\succ 0.259\right)$
$=1-P\left(Z<-0.259\right)$

Jeffrey Jordon