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CHAPTER PROBLEMS: PROBABILITIES
15 questions, 30 points
Chapter 05
Multiple Choice
1. Assuming the below results were obtained in a study used to test the accuracy of the rapid
diagnostic test for influenza, calculate and interpret the sensitivity of the rapid diagnostic
influenza test.
Frequency of Flu Cases
Frequency of Non-Flu Cases
Frequency of Individuals
Who Screened Positive
41
10
Frequency of Individuals
Who Screened Negative
51
100
a. When the rapid diagnostic influenza test is used, 53.22% of individuals who have the flu
test positive for the flu.
b. When the rapid diagnostic influenza test is used, 99.91% of individuals who have the flu
test positive for the.
c. When the rapid diagnostic influenza test is used, 44.57% of individuals who have the flu
test positive for the flu.
d. When the rapid diagnostic influenza test is used, 9.09% of individuals who have the flu
test positive for the flu.
2. Assume a cardiovascular surgeon has implanted 17 pacemakers in his patients from a new
batch of pacemakers that have been found to have a defect that causes them to stop working. If
each pacemaker has a 16.73% chance that it will work, what is the probability that all the
patients’ pacemakers will work the way they are supposed to?
a. 6.556e-9
b. .0537
c. 6.30e-14
d. .5470
3. Assuming you obtained a random sample of blood glucose levels from 32 individuals from a
population and the mean of the population is 120 and the standard deviation of the sample is 15,
calculate the probability that the mean blood glucose levels for the sample will be above 127.
a. .0041
b. .4100
c. .5900
d. .9959
4. As part of the study described in Problem 6, investigators wanted to assess the accuracy of
self-reported smoking status. Participants are asked whether they currently smoke or not. In
addition, laboratory tests are performed on hair samples to determine presence or absence of
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nicotine. The laboratory assessment is considered the gold standard, or truth about nicotine
consumption. The data are as follows:
Nicotine Absent
Nicotine Present
Self-reported nonsmoker
100
19
Self-reported smoker
18
52
What is the specificity of self-reported smoking status?
a. 1
b. 0.90
c. 0.85
d. 0.56
5. Diastolic blood pressures are assumed to follow a normal distribution with a mean of 90 and a
standard deviation of 14. What proportion of people has diastolic blood pressures less than 80?
a. 0.661
b. 0.894
c. 0.534
d. 0.238
6. The following table cross-classifies pregnant women in the study by their body mass index
(BMI) at 16 weeks gestation and whether they had pre-term delivery. What is the probability of
women with BMI less than 30 and delivers pre-term?
BMI < 30
BMI 30–34.9
BMI 35+
Pre-term
480
70
130
Full term
4800
460
280
a. 0.086
b. 0.077
c. 0.0493
d. 0.539
7. The following table cross-classifies pregnant women in the study by their body mass index
(BMI) at 16 weeks gestation and whether they had pre-term delivery. What proportion of women
with BMI greater than 35 delivers pre-term?
BMI < 30
BMI 30–34.9
BMI 35+
Pre-term
480
70
130
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Full term
4800
460
280
a. 0.0867
b. 0.293
c. 0.317
d. 0.429
8. High density lipoprotein (HDL) in healthy males follows a normal distribution with a mean of
50 and a standard deviation of 10. What proportion of healthy males has HDL exceeding 65?
a. 0.067
b. 1.00
c. 0.493
d. 0.293
9. An experimental drug has been shown to be 85% effective in eliminating symptoms of
allergies in animal studies. A small human study involving eight participants is conducted. What
is the probability that the drug is effective on half of the participants?
a. 0.132
b. 0.493
c. 0.40
d. 0.0185
10. A national survey of graduate students is conducted to assess their consumption of coffee.
The following table summarizes the data. What proportion of coffee drinkers (caffeinated and
decaffeinated) is female?
Do Not Drink Coffee
Drink Decaffeinated Only
Drink Caffeinated
Coffee
Male
145
94
365
Female
80
121
430
a. 0.70
b. 0.50
c. 0.90
d. 0.546
True/False
11. True or False? In stratified sampling, the population is split into non-overlapping groups or
strata (e.g., men and women; people under 30 years of age and people 30 years of age and older)
and then sample within each strata.
12. True or False? Sensitivity and specificity are both forms of conditional probability.
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13. True or False? In Simple random sampling, each member of the population is assigned a
unique identification number, and then a set of numbers is selected at random to determine the
individuals to be included in the sample.
14. True or False? "A percentile is a value in the distribution that holds a specified percentage of
the population above it."
15. True or False? The normal distribution model is an important probability distribution model
that is appropriate when a particular experiment or process results in a continuous outcome.
