GROUP WORK
1. Polygraph lie-detector machines are commonly used in criminal investigations. The device
measures nervous excitement, operating on the idea that if a person is telling the truth they will
remain calm.

The American Polygraph Association claims that polygraphs accurately identify liars 90% of the
time. In other words, if a person lied the test results will be positive 90% of the time.

Although the polygraph test is good at identifying liars, there is a 50% chance that the polygraph
test will say a truthful person is lying.
A police force wants to predict the accuracy of lie-detector tests for 1,000 suspected criminals. Assume that
700 per 1,000 suspected criminals tell the truth during polygraph tests.
(a) Complete the table.
(b) What is the value of P?
10
30
70
270
350
700
500
(c) What is the value of Q?
300
(d) What is the probability of a false positive test result? A false positive is the probability that a
person is telling the truth given that the test result is positive, P(truth given a positive test result).
350 out of 700
350 out of 1,000
1
350 out of 620
350 out of 380
2. The table below is based on a 1988 study of accident records conducted by the Florida State
Department of Highway Safety.
(a)
What is the explanatory variable? ________________________________________
What is the response variable?________________________________________
(b)
(c)
Does wearing a seat belt lower the risk of an accident resulting in a fatality? Which of the
following calculations are the most helpful for answering this question?
A. 510 / 412,878
and
B. 412,368 / 574,895 and
1,601 / 164,128
510 / 2,111
C. 510 / 577,066
D. 510 / 2,111
1,601 / 577,066
1,601 / 2,111
and
and
Decide whether the following statement is valid or invalid.
Based on this data, the risk of a fatal accident is very small whether you are wearing a seat
belt or not. Do you think this statement is valid or invalid? _____________
(d) Based on this data, the risk of fatal accident for those wearing seat belts decreases by ________
percent. Use the formula to caluculate the percentchage.
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3. The following table summarizes the full-time enrollment at a community college located in a
West Coast city. There are a total of 12,000 full-time students enrolled at the college. The two
categorical variables here are gender and program. The programs include academic and
vocational programs at the college. Assume that a student can enroll in only one program.
(a) What proportion of the total number of students are male students?
0.52
0.02
0.48
0.58
(b) What proportion of the total number of students are Arts-Sci students?
0.52
0.02
0.89
0.75
(c) Suppose we select a male student. What is the probability that he is in the Graphics Design
program?
97 out of 12000
97 out of 202
97 out of 105
97 out of 5802
(d) Suppose we select a student in the InfoTech program at random. What is the probability that the
student is male?
1058 out of 5802
564 out of 1058
564 out of 12000
564 out of 5082
(e) What is the probability that a randomly selected student is female and in the Bus-Econ program?
435 of 12000
435 of 925
925 of 12000
6198 of 12000
(f) Find P(male | Culinary Arts).
0.03
0.01
0.53
0.02
(g) If a student is selected at random, what is the probability that the student is female or in the
Culinary Arts program? Show your work.
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