Question

Scores on an English test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. Find the score that separates the top 59% from the bottom 41%

Answer 1

Given that,

mean = = 37.6

standard deviation = =7.6

Using standard normal table,

P(Z > z) =59 %

= 1 - P(Z < z) = 0.59

= P(Z < z ) = 1 - 0.59

= P(Z < z ) = 0.41

= P(Z <-0.23 ) = 0.41  

z = -0.23 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= -0.23 *7.6+37.6

x=35.852

x=35.9