Question

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with mean 24 and standard deviation 4. What ACT score should a student have in order to be in the top 5% of test takers? (use 3 decimals)

Answer 1

Solution:-

Given that,

mean = = 24

standard deviation = = 4

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95  

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 4 + 24

x = 30.58