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

Answer:

$P_{39}=133.68$    

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

$P( X < x) = P( z < \displaystyle\frac{x - 158.9}{90.4})=0.39$  

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

$\displaystyle\frac{x - 158.9}{90.4} = -0.279\\\\x = 133.6784\approx 133.68$  

$P_{39}=133.68$

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