Question

A distribution of scores in Sociology 100 for the past five years has a mean of 75 and a standard deviation of 20. What scores represent the middle 75% of the distribution?

Answer 1

Solution:-

Given that,

mean = = 75

standard deviation = = 20

n = 100

=   = 75

= / n = 20 / 100 = 2

Using standard normal table,

P( -z < Z < z) = 75%

= P(Z < z) - P(Z <-z ) = 0.75

= 2P(Z < z) - 1 = 0.75

= 2P(Z < z) = 1 + 0.75

= P(Z < z) = 1.75 / 2

= P(Z < z) = 0.875

= P(Z < 1.15) = 0.875

= z  ± 1.15

Using z-score formula  

= z * +

= -1.15 * 2 + 75

= 72.7

Using z-score formula  

= z * +

= 1.15 * 2 + 75

= 77.3

A middle 75% scores represents are 72.7 to 77.3.