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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.