Question

A population of values has a normal distribution with μ = 158.9 μ = 158.9 and σ = 90.4 σ = 90.4 . You intend to draw a random sample of size n = 218 n = 218 . Find P39, which is the mean separating the bottom 39% means from the top 61% means. P39 (for sample means) =

Answer 1

`P_(39)=133.68`

Explanation:

We are given the following information in the question:

Mean, μ = 158.9

Standard Deviation, σ = 90.4

We are given that the distribution is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

We have to find the value of x such that the probability is 0.39

`P( X < x) = P( z < \displaystyle(x - 158.9)/(90.4))=0.39`

Calculation the value from standard normal z table, we have,

`\displaystyle(x - 158.9)/(90.4) = -0.279\\\\x = 133.6784\approx 133.68`

`P_(39)=133.68`

133.68 separates the bottom 39% means from the top 61% means.