AP Statistics
Name: ___________________________
Test 1 (Probability and Data Analysis)
Block: _______
Be sure to show all of your work.
1. There are 8000 men and 10000 women attending a state university. If 43 percent of men and
27 percent of women are business majors, use this information to determine if the events of
being a man and being a business major are independent.
The expectation for this problem was to show one of the probability checks:
P(A and B) = P(A) x P(B)
P(A|B) = P(A)
P(B|A) = P(B)
All work should be shown, and the implication that if they are equal they are independent (or if they are
not equal they are not independent) needs to be stated.
2. A travel agent books passages on three different tours, with half her customers choosing tour
𝑇1 , one-third choosing 𝑇2 , and the rest choosing 𝑇3 . The agent has noted that three-quarters of
those who take tour 𝑇1 return to book passage again, two-thirds of those who take 𝑇2 return,
and one-half of those who take 𝑇3 return. If a customer does return, what is the probability that
the person first went on𝑇2 ? (Include the probability notation as part of your answer).
Most students choose to use a tree diagram here but any correct work is acceptable. The variable for
“returning” needs to be defined (if one is used), and the final answer would be some form of:
R=Return
𝑃(𝑇2 ∩𝑅)
𝑃(𝑅)
which is approximately .3265
3. There are two games involving flipping a fair coin. In the first game, you win a prize if you can
throw between 45 percent and 55 percent heads; in the second game, you win if you can throw
more than 60 percent heads. For each game, would you rather flip the coin 30 times or 300
times? Explain your reasoning for both answers.
Some explanation of the Law of Large numbers should be provided as the statistical reasoning for
flipping 300 times for the first game and 30 times for the second.
4. Out of the 2000 students at Lake Norman High School, 96 are currently taking AP Statistics, 92
are currently taking some form of AP Calculus, and 7 are currently taking both. Draw a Venn
diagram or a two-way table that shows the above information.
A two-way table or Venn diagram should be provided, however mistakes in the diagram do not carry
over to the probabilities below (that is, I check to see if the incorrect numbers are being used in the
probabilities below so that students are not losing points twice for the same mistake). Variables should
also be defined for the problem.
(Include the probability notation as part of your answer).
a. What proportion of students are taking both AP Statistics and AP Calculus?
C=Takes Calculus
S=Takes Statistics
𝑃(𝐶 ∩ 𝑆) =
7
2000
b. If a student is not taking AP Statistics, what is the chance they are taking AP Calculus?
𝑃(𝐶|𝑆 𝐶 ) =
85
1904
c. If a student is taking AP Calculus, what is the probability they are not taking AP
Statistics?
𝑃(𝑆 𝐶 |𝐶) =
85
92
5. The following table shows the survival status and class of passengers on the Titanic when it sank.
Class
Survived
Died
First
197
122
Second
94
167
Third
151
476
a. Give the marginal distribution of passengers by survival.
Survived:
442 or 442/1207
Died:
765 or 765/1207
b. Give the conditional distribution of passengers by class given that they survived.
6. If 𝑃(𝐴) = .25, and 𝑃(𝐵) = .34, what is 𝑃(𝐴 ∪ 𝐵) if A and B are independent?
All work is expected to show the final value of .505. Students should clearly demonstrate they
understand (even without context) that it is essential to know these two variables are independent, in
order to find the overlapping area P(A and B) and use this to find P(A or B). As well as demonstrate they
know the difference between “and” and “or” notation.
7. Mr. Suk has determined he is terrible at fantasy football. He has calculated that he only has an
11 percent chance of winning on any given week. Use the line from the random number table
below to simulate the 16 weeks of the fantasy football season for Mr. Suk and record the wins
and losses for that simulation.
96927 19931 36809 74192 77567 88741 48409 41903 43909 99477 25330 64359
This problem is entirely dependent on the explanation of their simulation and if it will actual
simulate the chance process above. Points were determined by the correctness of the
simulation, the work involved in carrying out the simulation, and the overall answer.
8. A student from another AP Statistics class described a distribution the following way:
̅ = 𝟐𝟑𝟎. 𝟗𝟒
𝒙
Evaluate their description of the distribution. Be sure to mention if there
𝑺𝒙 = 𝟕𝟓. 𝟔𝟒
is anything incorrect about the description and/or include any information that
n=31
is missing.
minX=31.4
The answer should detail that this student did not actually describe anything.
𝑸𝟏 = 𝟏𝟕𝟐. 𝟕
In order to determine the shape a graph should be provided. The shape
Med=251.2
should determine the center and spread, and outliers should be calculated.
𝑸𝟑 = 𝟐𝟖𝟐. 𝟔
Since none of that is provided, we should make a graph (box and whisker plot)
maxX=345.4
and determine outliers (which there are none). From this we can determine
the shape is most likely skewed left. Finally, since we know shape, we should
use median and IQR for center and spread.
9. Use the table below to describe the distribution of heart rates for a random sample of students
at LNHS.
54
70
75
89
61
70
75
91
62
71
76
92
63
71
78
93
63
71
79
93
63
72
80
95
64
73
82
97
65
73
84
98
67
74
85
103
68
74
87
110
Note: The data above is for the practice test, but the overall expectations are the same. For
some reason my final test did not save correctly and I lost the last two questions.
This problem is very much like the previous one. Students were to supply the correct
information that describes the distribution without contradicting themselves by supplying
information that would be relevant for distributions of different shapes. The question was
graded on the following:
 A graph (of any form, boxplot, stem and leaf, histogram, etc.)
 Shape of the distribution
 Any outliers for the distribution (and work provided, this is the only acceptable place to
list things like IQR if it is not the measure of spread we want for the distribution, or used
in the graph).
 Center (with label, and as appropriate for the distribution)
 Spread (with label, and as appropriate for the distribution)
10. As I said above, the last question is missing, but the expectations are very similar to those of
problems 8 and/or 9. Students should use practices from class to analyze the summary
provided and determine:
 Outliers are missing (and there is a range of outlier starting at 87500.
 Since there are outliers the Median is the appropriate center and IQR spread.
 The newspaper did a good/bad job (depending on how they analyze it). Either answer is
acceptable as long as it is backed with a statistics based argument.
 Some reasoning for how they would convey the distribution to the prospective resident
based on percentages above or below specific values (using Q1, Median, Q3, IQR, etc.)
There are only 4 parts that I graded on this question, if a student provided a full description
of the distribution (Shape, Outliers, Center, and Spread) but neglected to accurately
articulate the question in context, they still received a majority of the credit.