Question

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate?

Answer 1

Given that,

mean = = 25

standard deviation = = 4

Using standard normal table,

P(Z > z) = 30%

= 1 - P(Z < z) = 0.3

= P(Z < z ) = 1 - 0. 3

= P(Z < z ) = 0.7

= P(Z < 0.52 ) = 0.7

z = 0.52 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.52 *4 +25

x=27.08