Question

A population of values has a normal distribution with μ=172.6 and σ=36. You intend to draw a random sample of size n=192

Find P₈₂, which is the score separating the bottom 82% scores from the top 18% scores.
P₈₂ (for single values) = ____________

Find P₈₂, which is the mean separating the bottom 82% means from the top 18% means.
P₈₂ (for sample means) = ___________

Enter your answers as numbers accurate to 1 decimal place.

Answer 1

Given that,

mean = = 172.6

standard deviation = =36

Using standard normal table,

P(Z < z) =82%

= P(Z < z) = 0.82  

= P(Z < 0.92) = 0. 82

z = 0.92   

Using z-score formula  

x= z * +

x= 0.92*36+172.6

x= 205.7

(b)

n = 36

= 172.6

= / n = 192/36=32

Using standard normal table,

P(Z < z) =82%

= P(Z < z) = 0.82  

= P(Z < 0.92) = 0. 82

z = 0.92   

Using z-score formula  

= z * +

=0.92 *32+172.6

= 202.0