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

Question

A population of values has a normal distribution with $μ = 129.7$ and $σ = 7.7$ . 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.
$P (M < 130.9) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Answer 1

Step 1
Given Information:

μ = 129.7

σ = 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 - μ}{\frac{σ}{\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

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

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