AP Statistics Final Exam Review
1. The time required for the first stage on an assembly line is normally distributed with a mean of 32
minutes and variance of 6 minutes, while the time required for an independent second stage is
normally distributed with a mean of 43 minutes and a variance of 10 minutes. What is the
probability that the two stages take over 80 minutes?
a.
b.
c.
d.
e.
0.1056
0.1865
0.2593
0.3341
0.3773
2. Which of the following is most important in avoiding bias in surveying?
a. Picking a sampling method in which every combination of people has the same chance of
being selected
b. Care in choosing individuals who you feel are representative of the population in terms of
as many characteristics as you can list
c. Making sure every individual in the population of interest is invited to respond
d. Sending out a large enough number of surveys so that even if the response rate is low, you
will have sufficient numbers of responses to do statistical analysis
e. Making sure the wording is not so neutral as to bore respondents
3. A simple random sample is defined by:
a. The method of selection
b. Examination of the outcome
c. Whether or not a random number generator is used
d. How representative the sample is of the population
e. The assignment of different numbers associated with the outcomes of some chance
situation
4. The speeds of cars passing through an automated E-Z Pass tollbooth have a nearly normal
distribution with a mean of 5 mph and a standard deviation of 0.6 mph. What is a speed at the 30th
percentile?
a.
b.
c.
d.
e.
4.48 mph
4.69 mph
4.82 mph
5.31 mph
5.52 mph
8
5. Suppose we have a random variable X where the probability for k = 0, …, 8 is  (0.45) k (0.55) 8k .
k 
What is the mean of X?
a. 0.45
b. 0.55

c. 1.98
d. 3.6
e. 4.4
6. If quartiles Q1=20 and Q3=30, which of the following must be true?
I.
II.
III.
a.
b.
c.
d.
e.
The median is 25.
The mean is between 20 and 30.
The standard deviation is at most 10.
I only
II only
III only
All are true
None are true
7. A simple random sample of 35 world-ranked chess players provides the following statistics:
Number of hours of study per day: x  6.2, sx = 1.3
Yearly winnings: y  $208,000 , sy = $42,000
Correlation: r = 0.15
a.
b.
c.
d.
e.

Predicted winnings = 178,000 + 4850(Hours)

Predicted
winnings = 169,000 + 6300(Hours)
Predicted winnings = 14,500 + 31,200(Hours)
Predicted winnings = 7750 + 32,300(Hours)
Predicted winnings = -52,400 + 42,000(Hours)
8. A rural college is considering constructing a windmill to generate electricity but is concerned over
noise levels. A study is performed measuring noise levels (in decibels) at various distances (in
feet) from the campus library. Which of the following is a proper and most informative conclusion
for an observation with a negative residual?
a.
b.
c.
d.
e.
The measured noise level is 0.74 times the predicted noise level.
The predicted noise level is 0.74 times the measured noise level.
The measured noise level is greater than the predicted noise level.
The predicted noise level is greater than the measured noise level.
The slope of the regression line must be negative.
9. In the following table, what value of n results in a table showing perfect independence?
20
30
a.
b.
c.
d.
e.
10
40
60
75
100
50
n
10. A common classroom practice is to have students exchange their quizzes for grading. This
practice is hypothesized to reduce time between quiz and feedback to students, thus resulting in
higher achievement. Your history teacher, aware of your statistical prowess, has asked you to
design an experiment to test this theory. You have decided to use the final exam (not graded by
students) as your response measure. Your history teacher has three classes, one early in the
morning, one at noon, and one late in the afternoon. Each class contains 30 students.
a. Describe the treatments you will use in your experiment.
b. One possible confounding variable is the time of day; students may be more alert at certain
times of the day than at other times. Describe a method that could be used to control this
variable. Students have already been assigned their schedules, and these cannot be
changed.
c. Do you feel the results of your experiment could be generalized to Math classes? Explain
why or why not.
11. You are participating in the design of a medical experiment to investigate whether aspirin in the
diet will reduce the risk of people having heart disease. Outline the design of an appropriate
experiment with 100 participants. (Hint: include all key words in your design).
12. The Round Rock Express have a pitcher with an impressive winning record. Opposing teams are
attempting to analyze his pitches. The pitcher throws a strike 35% of the time. If the pitcher
throws a strike the next pitch is a fastball 40% of the time. If the pitcher doesn’t throw a strike the
next pitch is a fastball 80% of the time. What is the probability of him throwing a fastball? What is
the probability of him throwing a fastball given the previous pitch was not a strike? Given that the
second pitch was not a fastball, what is the probability that the first pitch was a strike?
13. In 1980 automobile registrations by states ranged from a low of 262,000 (Alaska) to a high of
16,873,000 (California) with a media of 2,329,000 (Iowa), a 25th percentile of 834,000 and a 75th
percentile of 3,749,000. In 1990, the registrations ranged from 462,000 (Vermont) to 21,926,000
(California) with a median of 2,649,000 (Oklahoma), a 25th percentile of 1,054,000, and a 75th
percentile of 4,444,000. Draw parallel boxplots and compare the distributions. (Hint: Do not forget
to check for outliers!)
14. An educational testing service has designed a new test of mechanical aptitude. Scores on this test
are normally distributed with 400 and  = 60.
a. What score would you need to be in the top 15%?
b. What score represents the 45th percentile?
c. 200 students at McCallum took the test, how many would you expect to score below 300?
15. Members of a group of 25 college students were classified according to hair and eye color as
follows:
Eye Color
Blue eyes
Green eyes
Red Hair
3
5
Blond hair
6
4
Brown hair
2
5
a. What is the probability that a member has red hair?
b. What is the probability that a member has blond hair and blue eyes?
c. What is the probability that a member has brown hair or green eyes, but not both?
d. Given that a member has blue eyes, what is the probability that he/she has red hair?
16. Car dealers across North America use the “Red Book” to help them determine the value of used
cars that their customers trade in when purchasing new cars. The book lists on a monthly basis
the amount paid at recent used-car auctions and indicates the values according to condition and
optional features, but does not inform the dealers as to how odometer readings affect the trade-in
value. In an experiment to determine whether the odometer reading should be included, ten 3year-old cars are randomly selected of the same make, condition, and options. The trade-in value
(in $100) and mileage (in 1000s of miles) are shown below.
Odometer 59 92 61 72 52 67 88 62 95 83
Trade-in
37 31 43 39 41 39 35 40 29 33
a. Find the sample regression line for determining how the odometer reading affects the
trade-in value of the car.
b. Interpret the slope in terms of the problem.
c. Calculate and interpret the correlation coefficient.
d. Calculate and interpret the coefficient of determination.
e. Predict the trade-in value of a car with 60,000 miles.
f. What would be the odometer reading of a car with a trade-in value of $4200?
REVIEW ANSWERS
1. A
10. (a) student vs. teacher grading
2. A
(c) no  not representative
3. A
11. Randomization, treatments, measurements,
4. B
comparing, replication, blocking, direct
5. D
control
6. C
12. Tree problem – 0.66, 0.8, 0.6176
7. A
14. (a) 462.186 (b) 392.46 (c) 9.558
8. D
students
9. D
15. (a) 0.32 (b) 0.24 (c) 0.44 (d)
3/11=0.27
16. (a) yˆ  56.205  0.2668x
(b) slope = -0.2668
(c) r = -0.8934
(d) r2 = 0.7982

(e) $4019.54
(f) 57,245.08
*part (a) used x = odometer
readingremember to
perform the regression again
for f!