Question

Need calculations and answer.

Scores on a particular test are normally distributed with a mean of 70 and an SD of 15. between what 2 scores would you expect 96% of the scores to fall between ______________ and ________.

Answer 1

Given that,

mean = = 70

standard deviation = = 15

middle 96% of score is

P(-z < Z < z) = 0.96

P(Z < z) - P(Z < -z) = 0.96

2 P(Z < z) - 1 = 0.96

2 P(Z < z) = 1 + 0.96 = 1.96

P(Z < z) = 1.96/ 2 = 0.98

P(Z < 2.05) = 0.98

z  ± 2.05

Using z-score formula  

x= +-z * +

x= 2.05*15+70

x= 100.75 and 39.25