Math 138 Final Exam Review
Although there are many problems on this review, it does not fully cover all the material in
MATH 138. For additional review problems, review your homework problems, projects, exams,
and other classroom handouts.
Unit 1
1) Classify the variables as categorical or quantitative:
a) name
b) employee ID number
c) annual income
2) A survey of patients at a hospital classified the patients by gender and blood type, as seen in
the table.
Gender
Male Female
Blood A
105
93
type
B
98
84
O
160
145
AB
15
18
a) What percentage of the patients with type-B blood are male?
b) What percentage of the female patients have type-O blood?
c) What percentage of the patients are male and have type-A blood?
d) What percentage of the patients are female or have type-O blood?
e) Give the conditional distribution of blood type for the males
f) Give the conditional distribution of blood type for the females
g) Are blood type and gender independent?
3) The number of days off that 30 police detectives took in a given year are provided below.
Create a histogram of the data. (You can do this by hand or using technology as long as the
bins are reasonable and you can reproduce an accurate sketch).
10
5
5
1
1
4
3
0
1
5
9
7
4
11
7
7
1
11
0
5
1
6
7
5
6
10
6
1
1
0
4) Describe what these boxplots tell you about the relationship between fuel efficiency and the
number of cylinders an engine has.
5) The stem-and –leaf diagram shows the ages of males playing basketball at a public gym over
the course of a day. Describe the shape, center, spread, and unusual features of the
distribution.
4 8 9
4 0 1 2 3
3 6 6 8 8 9
3 0 0 0 1 4 4
2 6 7 9 9 9
2
1 5 5 5 5 6 6 6 6 6 6 7 7 7
1 2 3 4 4 4 4
0
0
6) The volumes of soda in quart soda bottles can be described by a Normal model with a mean
of 32.3 oz and a standard deviation of 1.2 oz.
a) What percentage of bottles can we expect to have a volume less than 32 oz?
b) 5% of bottles have a volume smaller than what amount?
7) The ages of the 21 members of a track and field team are listed below.
15
24
28
18
24
28
18
25
30
19
25
32
22
26
33
23
26
40
24
27
42
a) Report the 5-Number Summary for the data
b) Create a boxplot for the data. Use fences to identify potential outliers, if there are any.
c) Find the mean and the standard deviation for the data
d) What is the z-score for the age of the team member who is 40 years old?
e) Interpret the meaning of this z-score.
8) The distances traveled to work in miles by the employees at a large company are normally
distributed with the mean of 35 ml. and standard deviation of 10 ml.
a) What is the z score of an employee who travels 40 miles?
b) What percent of employees travel more than 45miles ?
c) Find the 90th percentile of the travel distances
d) In what interval do the middle 70% of travel distances fall?
9) Match the given correlation coefficients with the scatter plots.
10) The attendance at Camden Yards during the 12 years from 2000 to 2011 is given as follows:
(Source: http://www.ballparksofbaseball.com/attendance.htm)
Year
Attendance
a) Find the equation of the regression line.
2000
3,296,031
2001
3,094,841
b) Interpret the slope in context.
2002
2,682,439
2003
2,454,523
c) Find and interpret the residual for 2008
2004
2,744,013
d) Overall, is this a good linear fit? Explain.
2005
2,624,804
2006
2,153,150
e) Is it feasible to use this model to predict attendance in 2014?
2007
2,164,822
Why or why not?
2008
1,950,075
2009
1,907,163
f) What is the predicted attendance for 2014? (The actual
2010
1,733,018
attendance was 2,102,240).
2011
1,755,461
11) The March 2000 Consumer Reports compared various brands of supermarket enchiladas in
cost and sodium content. Use the scatterplot and regression analysis to answer the questions.
Fitted Line Plot
Sodium content (mg) = 2185 - 607.0 Cost (per serving)
1750
S
R-Sq
R-Sq(adj)
Sodium content (mg)
1500
250.702
77.3%
74.0%
1250
1000
750
500
1.0
1.5
2.0
Cost (per serving)
2.5
3.0
a) Use the scatterplot above to describe the relationship between Cost and Sodium Content.
b) What is the correlation coefficient for the relationship between cost and sodium content?
c) How much sodium would you expect if the cost is $2.90?
Unit 2
12) A real estate company kept a database on the apartments in a certain city. The percentages of
various types of apartments are listed below.
Number of Percent
bedrooms
0 (Studio)
15.9
1
25.5
2
45.8
3
10.1
a) Are events represented in this table disjoint?
b) What is the probability that a randomly selected apartment in this city is a 1-bedroom or
2-bedroom apartment?
c) What is the expected value for the number of bedrooms that an apartment will have?
13) Explain the difference between an experiment and an observational study
14) Of the coffee makers sold in an appliance store, 6.0% have either a faulty switch or a
defective cord, 2.0% have a faulty switch, and 0.8% have both defects. What percent of the
coffee makers will have a defective cord?
15) Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail
presale testing.
a) What is the probability that the first chip fails and the second chip passes presale testing?
b) If you test 4 chips, what is the probability that not all of the chips fail?
16) Suppose that on any given day, there is a 65% chance of it being sunny, a 10% chance of
rain, and a 25% chance of being cloudy.
a) Clearly explain how you would use the random numbers from 1 to 100 to conduct a
simulation to model this situation
b) If you were asked to find the probability that it will sunny at least two days in a week,
clearly state what the response variable would be.
c) For each trial below, fill in the resulting outcome
Trial #
Random Numbers
1
2
3
4
5
6
65 91 5 72 41 69 48
90 82 93 74 63 67 71
34 35 56 83 42 4 95
91 42 18 37 81 85 67
80 57 63 38 76 35 12
63 84 65 36 82 89 68
Number of Sunny
Days
Response Variable
d) Using your simulation, estimate the probability that it will be sunny at least two days in a
week.
e) Using your simulation, how many sunny days would you estimate per week?
17) Assume that 11% of people are left-handed. If we select 10 people at random, find the
probability that
a) Exactly 3 are left-handed.
b) At most 2 are left-handed
c) At least 2 are left-handed
d) Between 1 and 4 people are left-handed (inclusive)
e) Explain how you know that the Binomial model applies to this situation
f) What is the mean and the standard deviation of the number of left-handed people in a
group of 10?
18) Suppose that in a given suburb 60% of the houses have garages, 40% have decks, and 30% of
the houses have both.
a) What is the probability that a randomly selected house has a garage or a deck?
b) What is the probability that a randomly selected house will have neither a garage nor a
deck?
c) What the probability that a randomly selected house will have a deck but not a garage?
d) What is the probability that a randomly selected house will have a deck if it is known that
the house has a garage?
e) Are the events of a house having a garage and a house having a deck independent?
Justify your answer with a probability test.
19) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are
selected at random from the physics majors, what is the probability that no more than 6
belong to an ethnic minority?
20) Suppose you buy 1 ticket for $1 out of a lottery of 100 tickets where the prize for the one
winning ticket is to be $50. What is your expected value?
21) A tax auditor has a pile of 191 tax returns of which he would like to select 17 for a special
audit. Describe a method for selecting the sample which involves
a) systematic sampling
b) stratified sampling
c) simple random sampling
22) At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school
administrator selects a random sample of 12 of the freshmen, 9 of the sophomores, 11 of the
juniors and 8 of the seniors. She then interviews all the students selected. Identify the type
of sampling used in this example.
23) A car insurance company is interested in the association between age and the frequency of
car accidents. They obtained the following sample data.
Number of
accidents in
past 3 years
0
1
More than 1
total
Age Group
Under 25 25-45 Over 45
74
89
82
18
8
12
8
3
6
100
100
100
total
245
38
17
300
a) What is the probability that a randomly selected participant was under age 25?
b) What is the probability that a randomly selected participant was under age 25 or in more
than 1 car accident?
c) What is the probability that a randomly selected participant was over age 45 and in 0 car
accidents?
d) What is the probability that a randomly selected participant was over age 45 if it is known
that they were in 0 car accidents?
e) Do the events of being over 45 and having had 0 accidents in the past 3 years appear to
be independent? Justify your answer using probabilities.
24) Suppose that in a given court system 20% of defendants are truly innocent and 80% of
defendants are truly guilty. Defendants are given the choice to plead innocent or plead
guilty. Suppose that defendants who are innocent plead innocent 99% of the time and that
defendants who are guilty plead innocent 70% of the time.
a) Find the probability that a defendant is guilty and pleads guilty
b) Find the probability that a defendant is innocent and pleads innocent
c) Find the probability that a defendant pleads innocent
d) Find the probability that a defendant who pleads innocent is actually innocent
Unit 3
25) Assume that 25% of students at a university wear contact lenses. We randomly select 200
students.
a) What is the mean and standard deviation of the proportion of students in this group who
may wear contact lenses?
b) What is the probability that we observe a sample proportion (𝑝̂ ) of 30% or more students
who wear contact lenses?
26) The number of hours per week that high school seniors spend on computers is normally
distributed, with a mean of 4 hours and a standard deviation of 2 hours. 60 students are
chosen at random. Let y be the mean number of hours spent on the computer for this group.
Find the probability that y is between 4.2 and 4.4 hours.
27) A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to
pollution of the lake. How large a sample should be tested in order to be 99% confident that
the true proportion of inedible fish is estimated to within 6%?
28) A mayoral election race is tightly contested. In a random sample of 2200 likely voters, 1144
said that they were planning to vote for the current mayor. Based on a 95% confidence
interval, would you claim that the mayor will win a majority of the votes? Explain.
29) 7 of 8,500 people vaccinated against a certain disease later developed the disease. 18 of
10,000 people vaccinated with a placebo later developed the disease. Test the claim that the
vaccine is effective in lowering the incidence of the disease. Use a significance level of 0.02.
30) Suppose the proportion of sophomores at a particular college who purchased used textbooks
in the past year is p s and the proportion of freshmen at the college who purchased used
textbooks in the past year is p f . A study found a 95% confidence interval for ps  p f is
0.235,0.427 .
Does this interval suggest that sophomores are more likely than freshmen to
buy used textbooks? Explain.
31) A skeptical paranormal researcher claims that the proportion of Americans that have seen a
UFO, p, is less than 4%. He surveys 500 randomly selected Americans and finds that 11 of
them claim to have seen a UFO.
a) What type of test would be appropriate
b) Write the hypotheses
c) Check the assumptions and conditions
d) Conduct the hypothesis test. Report the test statistic and p-value, sketch the curve, and
make an appropriate conclusion.
e) What type of error might have occurred?
32) A police officer pulls over an individual that was driving recklessly. The police office is
trying to determine if the individual should be arrested for driving under the influence of
alcohol. Given Null and alternative hypotheses below, identify the type of error:
Ho: The individual is not driving under the influence of alcohol.
Ha: The individual is driving under the influence alcohol.
a) The police officer determines that the individual should be arrested and is driving under
the influence of alcohol when the individual is not driving under the influence of alcohol.
b) The police officer determines that the individual should not be arrested and is not driving
under the influence of alcohol when the individual is under the influence of alcohol.
33) In the past, the mean running time for a certain type of flashlight battery has been 8.5 hours.
That manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has increased as a result. He
samples 30 newly produced batteries and find a sample mean of 9.2 hours with a standard
deviation of 0.6 hours.
a) What type of test would be appropriate?
b) Write the hypotheses:
c) Conduct the test (report the test statistic, p-value, sketch the curve, and write an
appropriate conclusion). You can assume that all assumptions and conditions have been
met.
34) Using the data below and a 0.05 significance level, test the claim that the responses occur
with percentages of 15%, 20%, 25%, 25%, and 15% respectively.
Response
A
B
C
D
E
Frequency
12 15 16 18 19
35) A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and
their competition scores were recorded before and after the training. The results are shown
below.
Subject A
B
C
D
E
F
G
Before
9.4 9.5 9.6 9.6 9.4 9.6 9.6
After
9.5 9.7 9.6 9.5 9.5 9.9 9.4
Do the data suggest that the training technique is effective in raising the gymnasts’ scores?
Perform a hypothesis test at the 5% significance level.
36) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was
240 milligrams with s  19.8 milligrams.
a) Construct a 95% confidence interval for the true mean cholesterol content of all such
eggs.
b) Interpret this confidence interval.
37) Suppose you have obtained a confidence interval for  , but wish to obtain a greater degree of
precision. Which of the following would result in a narrower confidence interval?
a)
b)
c)
d)
Increasing the sample size while keeping the confidence level fixed
Decreasing the sample size while keeping the confidence level fixed
Increasing the confidence level while keeping the sample size fixed
Decreasing the confidence level while keeping the sample size fixed
38) A car insurance company performed a study to determine whether an association exists
between age and the frequency of car accidents. They obtained the following sample data.
Perform a test to see if there is an association between age and frequency of car accidents.
  0.05
Age Group
Under 25 25-45 0ver 45 total
Number of
0
74
89
82
245
accidents in
1
18
8
12
38
past 3 years
More than 1
8
3
6
17
total
100
100
100
300