Question

Scores on an English test are normally distributed with a mean of 73.6 and a standard deviation of 8.5. Find the score that separates the top 20% from the bottom 80%.

Answer 1

Given that,

mean = = 73.6

standard deviation = =8.5.

Using standard normal table,

P(Z > z) =  20%

= 1 - P(Z < z) = 0.20

= P(Z < z ) = 1 - 0.20

= P(Z < z ) = 0.80

z =0.84 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.84*8.5.+73.6

x= 80.74