# A normal population has mean \mu = 20 and standard deviation \sigma = 4. What is the probability that a randomly chosen value will be greater than 25?

A normal population has mean $\mu =20$ and standard deviation $\sigma =4$.
What is the probability that a randomly chosen value will be greater than 25?
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Step 1
From the provided information,
Mean $\left(\mu \right)=20$
Standard deviation $\left(\sigma \right)=4$
$X\sim N\left(20,4\right)$
Step 2
The required probability that a randomly chosen value will be greater than 25 can be obtained as:
$P\left(X>25\right)=P\left(\frac{x-\mu }{\sigma }>\frac{25-20}{4}\right)$
$=P\left(Z>1.25\right)$
$=1-P\left(Z<1.25\right)$
$=1-0.8944=0.1056$ (Using standard normal table)
Thus, the required probability is 0.1056.

Jeffrey Jordon