Question

A population of values has a normal distribution with μ=125.4 and σ=90.4. You intend to draw a random sample of size n=115

Find P₂₈, which is the score separating the bottom 28% scores from the top 72% scores.
P₂₈ (for single values) =

Find P₂₈, which is the mean separating the bottom 28% means from the top 72% means.
P₂₈ (for sample means) =

Answer 1

Given that,

mean = = 125.4

standard deviation = = 90.4

n = 115

= 125.4

= / n = 90.4 /115=8.43

Using standard normal table,

P(Z < z) = 28%

= P(Z < z) = 0.28  

z =-0.58    Using standard normal table,

Using z-score formula  

= z * +   

= -0.58 *8.43+125.4

= 120.51