AP Statistics Review of Part II
1) Tony and Mark took different college entrance tests. The scores on the test that
Tony took are normally distributed with a mean of 25 points and a standard
deviation of 4.2 points. The scores on the test that Mark took are normally
distributed with a mean of 550 points and a standard deviation of 90 points. Tony
scored 30 on his test and Mark score 610 on his test. Who scored better on his
college entrance test? Explain your reasoning.
Tony
Mark
30  25
610  550
z
 1.19
z
 0.67
4.2
90
Tony scored better because he had a high z-score.
2) The score on an exam for entrance to a law enforcement program are normally
distributed with the mean of 250 points and standard deviation of 25 points.
a. Label the normal curve
b. What is the z-score for an entrance exam of 232?
z  .72
c. What percent of the population would have an entrance exam grade of a 289?
94.06%
d. What percent of the population had an entrance exam grade above 200?
97.72%
e. What percent of the population had an entrance exam grade between 235 and 260?
38.12%
f. Determine entrance exam score if you are in the 80th percentile.
271
g. Find the interval that contains the middle 95% of entrance exam scores?
The interval that contains the middle 95% of entrance exams is between 200 and 300
3) Managers rate employees according to job performance and attitude. The results for
several randomly selected employees are given below in the table. Answer the following
questions.
Attitude
59
63
65
69
58
77
76
69
70
64
Performance
72
67
78
82
75
87
92
83
87
78
a) What is the least square regression line?
performance  11.629  1.022attitude
b) Explain, in context, what the r value means.
r  0.863 indicates that there is a moderately strong, positive, linear relationship
between attitude and performance.
c) Explain, in context, what the R 2 value means.
r 2  0.745 indicates that indicates that 74.5% of the variation in the performance is accounted for by
the linear relationship with attitude.
d) Explain in context, what the slope of the line means.
The job performance 1.022 increases as the attitude increases
4) A survey of students in a large Introductory Statistics class asked about their birth order
(first or only child, second, etc.) and which major they were enrolled in.
Arts and sciences
Mathematics
Science
Other
Total
First or only
34
52
15
12
113
Second or later
23
41
28
18
110
Total
57
93
43
30
223
a) What is the probability that the person was enrolled in mathematics if it is known that
the person was a first or only child?
52
 0.460
113
b) What is the probability that the person was the first or only given that it is a person who
was a mathematics major?
52
 0.559
93
c) Are the events selecting a math major and selecting a person who was a first or only
child independent events? Justify your answer.
No because 0.460  0.559
5) Researchers believe that a new drug called Bone Builder will help bones heal after children have
broken or fractured a bone. The researchers believe that Bone Builder will work differently on
bone breaks than on bone fractures. On all subjects, Bone Builder will be used in conjunction with
traditional casts. To test the impact of Bone Builder on bone healing, the researchers recruit 18
children with bone breaks and 30 children with bone fractures. The time required for the bone to
completely heal from the time it was put in the cast will be measured.
Design an appropriate experiment to determine if Bone Builder will help bones heal?
Birthweights and Birth Order.
A physician who has delivered babies for over 20 years claims that the birthweights of babies tend
to be higher than the birthweight of their next older sibling. In other words, a parent’s second child
tends to have a higher birthweight than the first child, the third child tends to have higher
birthweight than the second child, and so on. To verify the doctor’s statement, her office assistant
gets a random sample of mothers with at least two children from the hospital records, and records
the birthweights of the first two children. The birthweights for the children of 19 mothers are given
in the table below.
Mother
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Birthweight of First
Child (in pounds)
Birthweight of Second
Child (in pounds)
5.13
5.25
6.71
4.71
3.77
5.81
8.29
6.36
6.08
4.91
3.19
5.64
6.37
5.90
4.73
5.60
4.68
7.79
4.18
5.37
5.65
6.89
5.61
3.37
6.65
8.77
6.13
6.97
5.58
3.43
5.89
6.88
6.21
4.93
6.25
5.30
7.38
4.77
44a. Does this data provide any evidence to support the physician’s theory? Justify your answer
using the following statistical evidence.
Write down the five number summary for each of the categories with the mean and
standard deviation. Each of the statistics in the Five-Number Summary is higher for the
second child that the corresponding statistic for the first child.
The boxplots illustrate this.
This data provides significant evidence SUPPORTING the physician’s statement
44b. The scatterplot of birthweights of first-born children and second-born children is given below.
Describe the relation between the birthweights of first-born children and the birthweights of
second-born children.
There appears to be a strong positive linear relationship between the birth weights of first and
second child.
44c. The regression analysis of the data resulted in the following outcome.
sec ond  0.55  0.967first
SD  0.3772
R 2  0.91
Is there a significant relation between the birthweights of the first-born children and the
birthweights of the second-born children? Justify your answer using statistical evidence.
The residual plot shows little to no pattern indicating that the linear model is appropriate.
We can conclude that there is sufficient evidence to indicate a relationship between
the birth weights of the second born child.
44d. Suppose the doctor is getting ready to deliver the second child of a mother whose first child
weighed 7.2 pounds. Predict the birthweight of this second child.