Question

A population of values has a normal distribution with μ=59 and σ=48.5. You intend to draw a random sample of size n=170.
Find P₈₁, which is the score separating the bottom 81% scores from the top 19% scores.
P₈₁ (for single values) =

Find P₈₁, which is the mean separating the bottom 81% means from the top 19% means.
P₈₁ (for sample means) =

Enter your answers as numbers accurate to 1 decimal place.
************NOTE************ round your answer to ONE digit after the decimal point! ***********
Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Given that,

mean = = 59

standard deviation = = 48.5

Using standard normal table,

P(Z < z) = 81%

= P(Z < z) = 0.81  

= P(Z <0.878 ) = 0.81

z = 0.878 Using standard normal table,

Using z-score formula  

x= z * +

x= 0.878*48.5+59

x= 101.583

x=101.6

(B)

n = 170

= 59

= / n = 48.5 /170=3.7198

Using standard normal table,

P(Z < z) = 81%

= P(Z < z) = 0.81  

= P(Z <0.878 ) = 0.81

z = 0.878 Using standard normal table,

Using z-score formula  

= z * +   

= 0.878*3.7198+59

= 62.3