Week 3 Problems
15 questions, 30 points
Place answers here
Chapter 5
1. A.
2. A. = (a binomial with n = 13, p = 0.2347, P(13 successes) = 6.556e-9 (really
small)
3. A.
4. D.
5. B.
6. C.
7. B.
8. D.
9. A.
10. D.
11. True
12. True
13. True
14. True
15. True
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 FluFrequency of Non-Flu
Cases Cases
Frequency of Individuals Who Screened
47 10
Positive
Frequency of Individuals Who Screened
43 100
Negative
A) When the rapid diagnostic influenza test is used, 52.22% of individuals who have the flu test
positive for the flu.
B) When the rapid diagnostic influenza test is used, 90.91% of individuals who have the flu test
positive for the.
C) When the rapid diagnostic influenza test is used, 47.78% 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 13 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 23.47% 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) .0527
C) .4730
D) .5270
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 population 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
nicotine. The laboratory assessment is considered the gold standard, or truth about nicotine
consumption. The data are as follows:
Nicotine Nicotine
Absent Present
Self-reported
90 17
nonsmoker
Self-reported smoker 10 50
What is the specificity of self-reported smoking status?
A)1
B)0.1
Pre-term
Full
term
A)0.0867
B)0.2857
C)0.0533
4700 480 300
C)0.84
D)0.90
5. Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a
standard deviation of 12. What proportion of people has diastolic blood pressures less than 80?
P (X< 80) = P (X < (80 – 85)/12) P(Z< -0.41666667), from p-value calculator = 0.3387
A)0.661
B)0.338
C)0.50
D)0.75
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 <BMI 30–BMI
30 34.9 35+
320 80 120
D)0.533
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 <BMI 30–BMI
30 34.9 35+
Pre-term 320 80 120
Full
4700 480 300
term
A)0.0867
B)0.2857
C)0.0533
D)0.533
8. High density lipoprotein (HDL) in healthy males follows a normal distribution with a mean of
50 and a standard deviation of 8. What proportion of healthy males has HDL exceeding 60?
(Using excel: = NORMSDISIT (-1.25)
A)0.50
B)1.00
C)0.894
D)0.106
9. An experimental drug has been shown to be 75% effective in eliminating symptoms of
allergies in animal studies. A small human study involving six participants is conducted. What is
the probability that the drug is effective on half of the participants?
A)0.132
B)0.868
C)0.50
D)0.20
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 Drink Decaffeinated Drink Caffeinated
Coffee Only Coffee
Male 145 94 365
Female 80 121 430
P(female/caffeinated and decaf)
=((121 + 430))/(215+ 795) = 0.546
14. True or False? A percentile is a value in the distribution that holds a specified percentage of
the population below it.
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.
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.
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.
