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PROBLEMS THAT APPEAR IN THE 9TH EDITION BUT NOT THE 8TH (OR VICE VERSA).
Exercise 4.8 (Abbreviated): We have defect data for 450 semiconductor wafers, some of which were made
from dies with particles on them.
The table reads:
Condition of Die
Quality
No Particles
Particles
Total
Good
320
14
334
Bad
80
36
116
Total
400
50
450
a. Give an example of a simple event
b. Give an example of a joint event
c. What is the complement of a good wafer?
d. Why is ‘good wafer’ and a die ‘with particles’ a joint event?
If a wafer is selected at random, what is the probability that:
e. It was produced from a die with no particles?
f. The wafer is bad?
g. The wafer is bad and it was produced from a die with no particles?
h. The wafer is good and it was produced from a die with no particles?
i. The wafer is good or it was produced from a die with no particles?
j. The wafer is bad or it was produced from a die with particles?
k. Explain the difference between the results in (h) and (i).
Exercise 4.9 (Abbreviated): A contingency table shows whether travel managers research or
book tickets on the internet.
The table reads:
Research Airline Tickets on
the Internet?
Yes
No
Total
Book Airline Tickets on the
Internet?
Yes
No
88
20
108
124
168
292
Total
212
188
400
a. Give an example of a simple event
b. Give an example of a joint event
c. What is the complement of “researches airline prices on the Internet”?
d. Why is “researches airline prices on the Internet” and “books airline tickets on the Internet” a joint event?
If a corporate travel manager is selected at random, what is the probability that he or she:
e. Researches airline prices on the Internet?
f. Books airline tickets on the Internet?
g. Researches airline prices on the Internet and books airline tickets on the Internet ?
h. Does not research airline prices on the Internet and does not book airline tickets on the Internet ?
i. Researches airline prices on the Internet or books airline tickets on the Internet ?
j. Does not research airline prices on the Internet or books airline tickets on the Internet ?
k. Explain the difference between the results in (g) and (i).
Exercise 4.14d (Would be 4.13d in 8th edition): Are the events A and B statistically independent?
Exercise 4.19: Repeat the table in 4.8.
The table reads:
Condition of Die
Quality
No Particles
Particles
Total
Good
320
14
334
Bad
80
36
116
Total
400
50
450
a. Suppose that you know a wafer is bad. What is the probability that it was produced from a die that had
particles?
b. Suppose that you know a wafer is good. What is the probability that it was produced from a die that had
particles?
c. Are the events ‘a wafer is good’ and ‘a die has no particles statistically independent? Explain.
Exercise 4.20: Repeat the table in 4.9.
The table reads:
Book Airline Tickets on the
Internet?
Yes
No
Research Airline Tickets on
Total
the Internet?
Yes
88
124
212
No
20
168
188
Total
108
292
400
a. Given that a corporate travel manager researched airline ticket prices on the internet, what is the
probability that he or she booked airline tickets on the internet?
b. Given that a corporate travel manager booked airline ticket prices on the internet, what is the probability
that he or she researched airline tickets on the internet?
c. Explain the difference in the results in (a) and (b).
d. Are the two events ‘researched airline tickets on the internet’ and ‘booked airline tickets on the internet’
independent? Explain.
Exercise 4.22: Of 56 white workers terminated, 29 claimed bias. Of 407 black workers terminated, 126
claimed bias.
a. Given that the worker is white, what is the probability that the worker claimed bias?
b. Given that the worker has claimed bias, what is the probability that the worker is white?
c. Explain the difference in the results in (a) and (b).
d. Are the two events ‘being white’ and ‘claiming bias’ statistically independent? Explain.
Exercise 4.65: In 1997, 24.0% of all highway fatalities involved a rollover. 15.8% of all accidents
involving a rollover involved SUVs, vans and pickups. Given that a rollover was not involved, 5.6% of
fatalities involved SUVs, vans and pickups. Define the following events:
{Fatality involved an SUV, van or pickup}
A
{Fatality involved a rollover}
B
a. Use Bayes’ theorem to find the probability that the fatality involved a rollover, given that the
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fatality involved an SUV, van or pickup.
b. Compare the result in (a) to the probability that the fatality involved a rollover, and comment
on whether SUVs, vans and pickups are more prone to rollover accidents.
Exercise 4.36(Not in 8th edition): If there are 10 multiple-choice questions on an exam, each having 3
possible answers, how many different possibilities are there for sequences of correct answers?
Exercise 4.39(Not in 8th edition): A brand of women’s jeans can be ordered in seven different sizes, 3
different colors and 3 different styles. How many jeans have to be ordered if the store wants to have one
pair of each type.
Exercise 4.43(Not in 8th edition): A gardener has 6 rows in his garden available for 6 different vegetables.
If each vegetable gets one row, how many different ways are there to position the vegetables in the garden?
Exercise 4.44(Not in 8th edition): The Big Triple consists of picking the correct order of finish of the first
3 horses in the 9th race. If there are 12 horses entered in the race, how many outcomes are there?
Exercise 4.45(Not in 8th edition): The Quinella consists of picking the horses that will place first or
second regardless of order. If 8 horses are entered in a race, how many winning combinations are there?
Exercise 5.18 (In 8th edition only): Suppose that a random sample of web surfers is selected and ask if the
remember a specific internet banner. Use the binomial model and assume that p  0.4.
a. What is the expected value or mean of this binomial distribution?
b. What is the standard deviation of this binomial distribution?
c. What is the probability that none of the surfers will remember the banner ad?
d. What is the probability that exactly one of the surfers will remember the banner ad?
e. What is the probability that exactly two of the surfers will remember the banner ad?
f. What is the probability that three or more of the surfers will remember the banner ad?
d. Assume that p  0.6. How does that change a-f.
Exercise 6.24 (Not in 8th edition): Suppose that you are sampling from a uniform distribution
with a  0 and b  10. What is the probability of obtaining a value:
a. between 5 and 7?
b. between 2 and 3?
c. What is the expected value?
d. What is the standard deviation?
Exercise 6.26 (Not in 8th edition): In a nuclear power plant seawater is used in cooling. The amount that
the water temperature is raised has a continuous uniform distribution over the interval between 10 to 25
degrees Celsius.
a. What is the probability that the temperature increase will be less than 20° C?
b. What is the probability that the temperature increase will be between 10 and 22° C?
c. Suppose that a temperature increase of more than 18° C is considered potentially dangerous?
What is the probability that the temperature increase is potentially dangerous?
d. What is the expected value of the temperature increase?
e. What is the standard deviation of the temperature increase?
Exercise 6.57(Not in 8th edition): An airline has 3 different choices on its dessert menu. Each dessert is
equally likely to be chosen.
a. If a random sample of 4 passengers is chosen, what is the probability that at least 2 will choose ice cream
for dessert?
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b. If a random sample of 21 passengers is chosen, what is the approximate probability that at least 2 will
choose ice cream for dessert?
Exercise 6.60(Not in 8th edition): The number of cars arriving per minute at a toll booth is Poisson
distributed with a mean of 2.5. What is the probability that in any given minute
a. No cars arrive.
b. Not more than 2 cars arrive?
c. What is the approximate probability that in a ten minute period not more than 20 cars arrive?
d. What is the approximate probability that in a ten minute period between 20 and 30 cars arrive?
Exercise 8.17(in 8th edition only): In order to estimate dental expenses to plan for a proposed dental plan,
a personnel department takes a random sample of dental expenses for the families of 10 employees over the
previous year. (Dental data set on disk)
Expenses
110
362
246
85
510
208
173
425
316
179
a. Set up a 90% confidence interval estimate of mean family dental exposes for all employees.
b. What assumption must be made about the population distribution in a)?
c. Give an example of a family dental expense that is outside the confidence interval but that are not unusual
for an individual family and explain why this is not a contradiction.
d. Repeat a) for a 95% interval.
e. What would the effect be in a) of changing the fourth value from $85 to $585?
Exercise 8.20(in 9th edition only): In New York a random sample was taken of the time required in days
to approve 27 Savings Bank Life Insurance policies. (Insurance data set on disk)
Time
73
31
92
19
56
63
16
22
50
64
18
51
28
45
69
28
48
16
31
17
17
90
17
60
17
56
91
a. Set up a 95% confidence interval estimate of mean processing time.
b. What assumption must be made about the population distribution in a)?
c. Do you think that the assumption made in b) has been seriously violated? Explain.
d. Compare the conclusions reached in a) with those of Problem 3.61 on page 126.
Downing and Clark, Old Computational Problem 1: For the sample data below b) Compute Covx, y 
and Corr x, y  . c) Compute the mean of x  y  and Var x  y  .
x 34 26 9 30 47 10 34 34 45 10 47 37 47 8 45
y 6 57 89 60 95 42 31 28 90 25 45 23 52 95 48
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