A population of values has a normal distribution with \mu=13.2 and \sigma=5.

A population of values has a normal distribution with $\mu =13.2$ and $\sigma =5$. You intend to draw a random sample of size $n=60$.
Find the probability that a sample of size $n=60$ is randomly selected with a mean between 11.5 and 14.
$P\left(11.5?

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joshyoung05M

The probability that mean value is between 11.5 and 14 is 0.8884, which is obtained below:
$P\left(x1<\stackrel{―}{X}
$P\left(11.5<\stackrel{―}{X}<14\right)=P\left(\frac{11.5-13.2}{\frac{5}{\sqrt{60}}}
$=P\left(-2.636

$=0.89251-0.00415=0.8884.$