# A population of values has a normal distribution with \mu=29.3 and \sigma=65.1. You intend to draw a random sample of size n=142.

A population of values has a normal distribution with $\mu =29.3$ and $\sigma =65.1$. You intend to draw a random sample of size $n=142$.
Find the probability that a sample of size n=142 is randomly selected with a mean between 27.7 and 35.3.
$P\left(27.7<\stackrel{―}{X}<35.3\right)=$?

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Step 1
According to the provided information,
$\mu =29.3$
$\sigma =65.1$
$n=142$
$P\left(27.7
$=P\left(-0.29
$=0.4784$ (From standard normal table)
Therefore, the probability that a sample of size $n=142$ is randomly selected with a mean between 27.7 and 35.3.
$P\left(27.7<\stackrel{―}{X}<35.3\right)=0.4784$

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