Question

1. A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the criminal behavior. It has an approximately normal distribution with a mean of 140 and a standard deviation of 40. (worth 12 points total

What proportion of respondents should score between 140 and 195? How would you interpret that proportion?

Answer 1

Given :- = 140 , = 40 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 140 < X < 195 ) = P ( Z < ( 195 - 140 ) / 40 ) - P ( Z < ( 140 - 140 ) / 40 )
= P ( Z < 1.38) - P ( Z < 0 )
= 0.9162 - 0.5 (From Z table)
= 0.4162

proportion of respondents who score between 140 and 195 is 0.4162