Show your steps in reasoning/computation. Draw a distribution, mark the z score

Question

Show your steps in reasoning/computation. Draw a distribution, mark the z score and/or area of question when appropriate (no need to turn it in). Round the results to two decimal points. Prison officials collect data for length of inmate prison term, in months, for various crimes. The data, which are approximately normally distributed, are listed below. The following convictions and sentences have just been issued: John, robbery, 62 months Pete, manslaughter, 123 months Clyde, assault, 43 months Maurice, drug dealing, 47 months Relatively, which convict received the harshest sentence? John scores 124 on an IQ test. He scores 6.2 on a reading achievement test. He scores 71 on math achievement test. The means and standard deviations for the three tests are as follows: What percentage of the population would be expected to score LOWER than John in IQ? What percentage of the population would be expected to score between the mean and John's IQ score? Given John's IQ, is his READING performance better, worse, or the same as you would expect? Given John's IQ, is his MATH performance better, worse, or the same as you would expect? Transform John's reading and math scores to the same scale as IQ, that is. M = 100. SD = 16.

Explanation / Answer

Result:

1).

For John, z = (62-58)/7 =0.57

For Pete, z = (123-112)/13 =0.85

For Clyde, z = (43-38)/4 =1.25

For Maurice, z = (47-43)/5 =0.8

Clyde received harshest sentence because his z score is largest.

2).

a). z for IQ score z =(124-100)/16 =1.5

P( x <124) = P( z <1.5) =0.9332

93.32%

b).

below mean scored are 50%

person sored between mean and Johns IQ score is 93.32-50

=43.32%

c).

z for reading score, z =(6.2-6.5)/6 = -0.05

z for reading score is lower than IQ score.

Reading score is worse.

d).

z for math score, z =(71-50)/14 = 1.5

z for Math score is same as IQ score.

Reading score is same as IQ score.

e).

x=mean+z*sd

reading score, x =100-0.05*16

=99.2

math score, x =100+1.5*16

=124

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.