Question

A normal distribution has a mean of 80 with a standard deviation of 20. What score separates the highest 40% of the distribution from the rest of the scores?

A) X= 54.4

B) X= 85

C) X= 75

D) X= 105.6

Answer 1

Given that,

mean = = 80

standard deviation = = 20

Using standard normal table,

P(Z > z) = 40%

= 1 - P(Z < z) = 0.40  

= P(Z < z ) = 1 - 0.40

= P(Z < z ) = 0.60

= P(Z < 0.25) = 0.60

z = 0.25

Using z-score formula  

x = z +

x = 0.25*20+80

x = 85