Question

1. A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed (meaning that the scores are normally distributed) so that it has a mean of 140 and a standard deviation of 40.a

. What is the percentile rank of a score of 172 (hint: as we covered in class, first figure out the percentage of scores falls below 172)? Show your work.

b. What is the probability of a randomly selected person scoring between 100 and 160? Show your work.

c. What is the probability of a randomly selected person scoring above 125? Show your work.

Answer 1

Solution :

Given that ,

mean = = 140

standard deviation = =  40

P(X< 172) = P[(X- ) / < (172 -140) / 40]

= P(z < 0.8)

Using z table

= 0.7881

probability=0.7881

(b)
P(100 < x <160 ) = P[(100 -140)/ 40) < (x -   ) /    < (160 -140) / 40) ]

= P(-1 < z <0.5 )

= P(z <0.5 ) - P(z <-1 )

Using z table,

=0.6915-0.1587

=0.5328

probability=0.5328

(c)P(x >125 ) = 1 - P(x< 125)

= 1 - P[(x -) / < (125 -140) /40 ]

= 1 - P(z < -0.375)

Using z table

= 1 - 0.3538

= 0.6462

probability= 0.6462