# A population of values has a normal distribution with \mu=129.7 and \sigma=7.7. You inte

A population of values has a normal distribution with $\mu =129.7$ and $\sigma =7.7$. You intend to draw a random sample of size $n=10$.
Find the probability that a sample of size $n=10$ is randomly selected with a mean less than 130.9.
$P\left(M<130.9\right)=$?

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Step 1
Given Information:
$\mu =129.7$
$\sigma =7.7$
$n=10$
Step 2
The probability that a sample of size $n=10$ is randomly selected with a mean less than 130.9.
$z=\frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}=\frac{130.9-129.7}{\frac{7.7}{\sqrt{n}}}=0.4928$
By referring to the z distribution, the p-value at $z=0.492$ is 0.311
Therefore, The probability that a sample of size $n=10$ is randomly selected with a mean less than 130.9 is 0.311