Math 160 Midterm Review
Multiple Choice: Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate response
1. The following frequency distribution analyzes the scores on a math test. Find the class
boundaries of scores interval 40 – 59.
Scores
40-59
60-75
76-82
83-94
95-99
A.
B.
C.
D.
Number of
Students
2
4
6
15
5
39.5, 58.5
40.5, 59.5
39.5, 59.5
40.5, 58.5
2. The frequency distribution below summarizes employee years of service for Alpha
Corporation. Determine the width of each class.
Years of
Service
1-5
6-10
11-15
16-20
21-25
26-30
A.
B.
C.
D.
6
4
5
10
Frequency
5
20
25
10
5
3
3. The frequency distribution for the weekly incomes of students with part-time jobs is given
below. Construct the corresponding relative frequency distribution. Round relative
frequencies to the nearest hundredth of a percent if necessary.
Income ($)
200-300
301-400
401-500
501-600
More than 600
Frequency
60
73
91
89
15
A.
Income ($)
200-300
301-400
401-500
501-600
More than 600
Relative
Frequency
18.29%
22.26%
27.74%
27.13%
4.57%
B.
Income ($)
200-300
301-400
401-500
501-600
More than 600
Relative
Frequency
12.5%
20.1%
37.3%
15.2%
14.9%
C.
Income ($)
200-300
301-400
401-500
501-600
More than 600
Relative
Frequency
15.5%
22.1%
31.3%
16.2%
14.9%
D.
Income ($)
200-300
301-400
Relative
Frequency
27.33%
27.38%
Income ($)
401-500
501-600
More than 600
Relative
Frequency
4.60%
18.07%
27.41%
4. A nurse measured the blood pressure of each person who visited her clinic. Following is a
relative-frequency histogram for the systolic blood pressure readings for those people aged
between 25 and 40. The blood pressure readings were given to the nearest whole number.
Approximately what percentage of the people aged 25-40 had a systolic blood pressure
reading between 110 and 139 inclusive?
A.
B.
C.
D.
75%
89%
39%
59%
5. In a survey, 20 people were asked how many magazines they had purchased during the
previous year. The results are shown below. Construct a histogram to represent the data.
Use 4 classes with a class width of 10, and begin with a lower class limit of -0.5. What is the
approximate amount at the center?
6, 15, 3, 36, 25, 18, 12, 18, 5, 30, 24, 7, 0, 22, 33, 24, 19, 4, 12, 9
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
the question.
Find the original data from the stem plot
6.
Stem
9
10
11
A.
B.
C.
D.
Leaves
59
19
55
95, 91, 99, 101, 111, 115
95, 99, 101, 109, 115, 115
95, 99, 101, 101, 115, 115
91, 95, 91, 109, 119, 115
Construct a pie chart representing the given data set.
7. The following data give the distribution of the types of houses in a town containing 44,000
houses.
Capes – 11,000
Garrisons – 15,400
Splits – 17,699
Find the mean for the given sample data. Unless indicated otherwise, round your answer to
one more decimal place than is present in the original data values.
8. Andrew asked seven of his friends how many cousins they had. The results are listed below.
Find the mean number of cousins.
18, 12, 7, 13, 7, 2, 7
A.
B.
C.
D.
9.4 Cousins
11 cousins
10.9 cousins
8.9 cousins
Find the median for the given sample data
9. The distances (in miles) driven in the past week by each of a company's sales
representatives are listed below.
107, 114, 214, 230, 436, 445
Find the Media Distance driven:
A.
B.
C.
D.
222 mi
220.50 mi
230 mi
214 mi
Find the mode(s) for the given sample data
10. Last year, nine employees of an electronics company retired. Their ages at retirement are
listed below.
53, 65, 63, 50, 56, 67, 62, 58, 54
A.
B.
C.
D.
53 yr, 65 yr, 63 yr, 50 yr, 56 yr, 67 yr, 62 yr, 58 yr, 54 yr.
58 yr
58.7 yr
No mode
Find the midrange for the given sample data
11. A meteorologist records the number of clear days in a given year in each of 21 different U.S.
cities. The results are shown below. Find the midrange.
72, 143, 52, 84, 100, 98, 101, 120, 99, 121, 86, 60, 59, 71, 125, 130, 104, 74, 83, 55, 169
A.
B.
C.
D.
110.5 days
117 days
112 days
98 days
Find the mean of the data summarized in the given frequency distribution
12. The highway speeds of 100 cars are summarized in the frequency distribution below. Find
the mean speed.
Speed (mph)
30-39
Cars
4
Speed (mph)
40-49
50-59
60-69
70-79
A.
B.
C.
D.
Cars
19
50
15
12
61.3 mph
58.5 mph
55.7 mph
54.5 mph
Find the range for the given sample data.
13. Jorge has his own business as a painter. The amounts he made in the last five months are
shown below.
$2416, $2423, $1644, $2036, $1267
A.
B.
C.
D.
$1149
$1156
$779
$772
Find the standard deviation for the given sample data. Round your answer to one more
decimal place than is present in the original data.
14. Christine is currently taking college astronomy. The instructor often gives quizzes. On the
past seven quizzes, Christine got the following scores:
50, 15, 31, 27, 11, 42, 71
A.
B.
C.
D.
11,341
31
20.9
8715.6
Find the standard deviation of the data summarized in the given frequency distribution.
15. A company had 80 employees whose salaries are summarized in the frequency distribution
below. Find the standard deviation.
Salary (dollars)
5001- 10000
10001 – 15000
Employees
12
13
A.
B.
C.
D.
Salary (dollars)
15001 – 20000
20001 – 25000
25001 – 30000
$7674.1
$7461.0
$7105.7
$7887.3
Employees
14
19
22
Use the range rule of thumb to estimate the standard deviation. Round results to the nearest
tenth.
16. The race speeds for the top eight cars in a 200-rnile race are listed below.
185.9, 179.5, 189.2, 176.7, 175.6, 188.7, 186.3, 177.9
A.
B.
C.
D.
1.1
7.5
6.8
3.4
Use the empirical rule to solve the problem.
17. At one college, GP A's are normally distributed with a mean of 2.9 and a standard deviation
of 0.6. What percentage of students at the college have a GP A between 2.3 and 3.5?
A.
B.
C.
D.
84.13%
68%
99.7%
95%
Solve the problem. Round results to the nearest hundredth.
18. The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The
team's center is 6.7 feet tall. Find the center's z score. Is his score unusual?
A.
B.
C.
D.
2.98, no
3, no
3.5, yes
3.85, yes
Find the number of standard deviations from the mean. Round your answer to two decimal
places.
19. The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10
inches. Last year there were 63 inches of snow. How many standard deviations from the
mean is that?
A.
B.
C.
D.
0.44 standard deviations above the mean
2.50 standard deviations below the mean
0.44 standard deviations below the mean
2.50 standard deviations above the mean
Determine which score corresponds to the higher relative position.
20. Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a
score of 82 on a test with a mean of 75 and a standard deviation of 4?
A. The first 82
B. The second 82
C. Both scores have the same relative position
Find the percentile for the data value.
21. Date set: 4, 6, 14, 10, 4, 10, 18, 18, 22, 6, 6, 18, 12, 2, 18;
Data value: 14
A.
B.
C.
D.
52
35
60
70
Find the indicated measure.
22. The test scores of 40 students are listed below. Find P56.
30, 35, 43, 44, 47, 48, 54, 55, 56, 57, 59, 62, 63, 65, 66, 68, 69, 71, 72, 72, 73, 74, 76, 77, 77, 78,
79, 80, 81, 81, 82, 83, 85, 89, 92, 93, 94, 97, 98
A.
B.
C.
D.
73
22.4
73.5
74
Construct a boxplot for the given data. Include values of the 5-number summary in all
boxplots.
23. The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown
below. Construct a boxplot for the data set.
310, 320, 450, 460, 470, 500, 520, 540,580, 600, 650, 700, 710, 840, 870, 900, 1000, 1200,
1250, 1300, 1400, 1720, 2500, 3700
Find the indicated probability.
24. A class consists of 66 women and 98 men. If a student is randomly selected, what is the
probability that the student is a woman?
A.
B.
C.
D.
49/82
33/82
1/164
33/49
Find the mean of the given probability distribution
25. The number of golf balls ordered by customers of a pro shop has the following probability
distribution.
X
3
6
9
12
15
A. μ = 6.99
B. μ = 9
P(x)
0.14
0.05
0.36
0.35
0.10
C. μ = 7.86
D. μ = 9.66
Provide an appropriate response. Round to the nearest hundredth.
26. The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective
computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the standard
deviation for the probability distribution.
A.
B.
C.
D.
  1.05
  0.59
  0.71
  0.77
Provide an appropriate response.
27. In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8.
What is your expected value?
A.
B.
C.
D.
-$5.17
$2.61
-$7.78
$10.39
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the
binomial probability formula to find the probability of x successes given the probability p of
success on a single trial. Round to three decimal places.
28. N = 12, x = 5, p= 0.25
A.
B.
C.
D.
0.091
0.082
0.103
0.027
Solve the problem
29. According to a college survey, 22% of all students work full time. Find the mean for the
number of students who work full time in samples of size 16.
A.
B.
C.
D.
2.8
3.5
0.2
4.0
30. The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches
of 8. Find the standard deviation for the number of seeds germinating in each batch.
A. 1.7
B. 1.3
C. 2.8
D. 16.8
31. On a multiple choice test with 19 questions, each question has four possible answers, one
of which is correct. For students who guess at all answers, find the mean for the number of
correct answers.
A.
B.
C.
D.
4.8
14.3
9.5
6.3
Determine if the outcome is unusual. Consider as unusual any result that differs from the
mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2 
or greater than μ+ 2  .
32. A survey for brand recognition is done and it is determined that 68% of consumers have
heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be
conducted. For such groups of 800, would it be unusual to get 698 consumers who
recognize the Dull Computer Company name?
A. Yes
B. No
Find the indicated z score. The graph depicts the standard normal distribution with mean O
and standard deviation 1.
33. Shaded area is 0.9599
A.
B.
C.
D.
1.82
1.03
-1.38
1.75
If z is a standard normal variable, find the probability.
34. The probability that z lies between 0.7 and 1.98
A.
B.
C.
D.
-0.2181
0.2175
1.7341
0.2181
Solve the problem. Round to the nearest tenth unless indicated otherwise.
35. In one region, the September energy consumption levels for single-family homes are found
to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.
Find P45, which is the consumption level separating the bottom 45% from the top 55%.
A.
B.
C.
D.
1078.3
1021.7
1148.1
1087.8
36. Scores on a test are normally distributed with a mean of 70 and a standard deviation of
11.5. Find P31, which separates the bottom 81% from the top 19%.
A.
B.
C.
D.
0.88
0.291
80.1
73.3
Assume that X has a normal distribution, and find the indicated probability.
37. The mean is μ= 15.2 and the standard deviation is  = 0.9. Find the probability that X is
greater than 17.
A.
B.
C.
D.
0.9713
0.9772
0.0228
0.9821
Find the indicated probability
38. The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a
standard deviation of $150. What percentage of trainees earn less than $900 a month?
A.
B.
C.
D.
40.82%
35.31%
90.82%
9.18%
Solve the problem
39. The amount of snowfall falling in a certain mountain range is normally distributed with a
mean of 94 inches, and a standard deviation of 14 inches. What is the probability that the
mean annual snowfall during 49 randomly picked years will exceed 96.8 inches?
A.
B.
C.
D.
0.0808
0.0026
0.4192
0.5808
40. The weights of the fish in a certain lake are normally distributed with a mean of 19 lb and a
standard deviation of 6. If 4 fish are randomly selected, what is the probability that the
mean weight will be between 16.6 and 22.6 lb?
A.
B.
C.
D.
0.6730
0.4032
0.0968
0.3270
Answer Key
1) C
2) C
3) A
4) A
5) The approximate amount at the center is 16 magazines.
6) B
7) A
8) A
9) A
10) D
11) A
12) C
13) B
14) C
15) C
16) D
17) B
18) C
19) D
20) B
21) C
22) D
23) C
24) B
25) D
26) D
27) A
28) C
29) B
30) B
31) A
32) A
33) D
34) D
35) B
36) C
37) C
38) D
39) A
40) A