A comprehensive study of juvenile delinquency is conducted i

A comprehensive study of juvenile delinquency is conducted in every state-run reform school in Ireland. A scale called the Antisocial Beliefs Scale is given to all juvenile delinquents. The mean (?) of the scale is 91 and the standard deviation (?) is 14. Assuming that the scores are normally distributed, what PERCENTAGE of the population scores are above 105?

Solution

Normal Distribution
Mean ( u ) =91
Standard Deviation ( sd )=14
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

P(X > 105) = (105-91)/14
= 14/14 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587                  

15.87 are above 105