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Fall Semester Final Exam 2012 Review #1
Name: __________________________ Date: _____________
___ 1. Find the sample variance s2 for the following sample data. Round your answer to the nearest
hundredth.
x:
23
20
14
35
25
A) 47.44
B) 81.66
C) 102.08
D) 59.30
E) 86.21
___ 2. True or false. The probability of some event is 80%.
A) false
B) true
___ 3. Suppose automobile insurance companies gave annual premiums for top-rated companies in several
states. The figure below shows box plots for the annual premium for urban customers in three states.
Which state has the smallest interquartile range?
A) Pennsylvania has the smallest interquartile range.
B) Texas has the smallest interquartile range.
C) Pennsylvania as well as California have the smallest interquartile range.
D) California has the smallest interquartile range.
E) none of these choices
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Fall Semester Final Exam 2012 Review #1
___ 4. A survey of 1000 adults uncovered some interesting housekeeping secrets. When unexpected
company comes, where do we hide the mess? The survey showed that 68 % of the adults toss their
mess in the closet, 23 % shove things under bed, 6 % put things in the bathtub, and 3 % put the
mess in the freezer. Make a circle graph to display this information.
A)
B)
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Fall Semester Final Exam 2012 Review #1
C)
D)
E) none of these choices
___ 5. Consider a binomial distribution with 11 trials. Look at a table showing binomial probabilities for
various values of p, the probability of success on a single trial. For what value of p is the distribution
symmetric?
A) p = 0.10
B) p = 0.01
C) p = 0.50
D) p = 0.05
E) p = 0.85
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Fall Semester Final Exam 2012 Review #1
___ 6. In your biology class, your final grade is based on several things: a lab score, score on two major
tests, and your score on the final exam. There are 100 points available for each score. However, the
lab score is worth 20% of your total grade, each major test is worth 27.5%, and the final exam is
worth 25%. Compute the weighted average for the following scores: 94 on the lab, 82 on the first
major test, 95 on the second major test, and 83 on the final exam. Round your answer to the nearest
hundredth.
A) 90.97
B) 86.02
C) 88.77
D) 88.22
E) 84.65
___ 7. Give an example of a continuous random variable.
A) The number of fish caught by a fishing boat
B) The number of coins contained in a slot machine
C) The number of traffic accidents in a city
D) The number of gallons of water in a reservoir
E) The number of tables sold at a furniture store
___ 8. True or false. The law of large numbers states that in the long run, as the sample size or number of
trials increases, the relative frequency of outcomes gets closer to the theoretical probability of the
outcome.
A) true
B) false
___ 9. The heights of 18-year-old men are approximately normally distributed with mean 68 inches and
standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at
random is between 64 inches and 68 inches?
A) 0.5918
B) 0.0918
C) 0.4082
D) 0.7162
E) 0.4202
___ 10. Richard has been given a 7-question multiple-choice quiz in his history class. Each question has four
answers, of which only one is correct. Since Richard has
not attended the class recently, he doesn't know any of the answers. What is considered the success?
A) number of questions
B) Richard answers a question correctly.
C) number of questions answered
D) Richard is unable to answer a question correctly.
E) none of the choices
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Fall Semester Final Exam 2012 Review #1
___ 11. Suppose that about 22% of those called will find an excuse (work, poor health, travel out of town,
etc.) to avoid jury duty. If 14 people are called for jury duty, what is the probability that all 14 will
be available to serve on the jury? Round your answer to three decimal places.
A) 0.024
B) 0.031
C) 0.000
D) 0.040
E) 1.000
___ 12. Identify the sampling technique used in the following information.
An important part of employee compensation is a benefits package that might include health
insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc.
Suppose you want to conduct a survey of benefits packages available in private businesses in
Hawaii. You want a sample size of 100. Sampling technique used to get the sample size of 100 is
described below.
Assign each business in the Island Business Directory a number, and then use a random-number
table to select the business to be included in the sample.
A) Cluster sample
B) Convenience sample
C) Simple random sample
D) Systematic sample
E) Stratified sample
___ 13. Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose for
healthy females, x has an approximately normal distribution with mean μ = 5 and standard deviation
σ = 0.3. Convert the following x interval from a laboratory test to a z interval.
3.8 < x
A)
B)
C)
D)
E)
–4 < z
–2 > z
1< z
–3 > z
–4 > z
___ 14. Assuming that the heights of college women are normally distributed with mean 60 inches and
standard deviation 3.5 inches, what percentage of women are taller than 53 inches?
A) 99.9%
B) 97.7%
C) 0.1%
D) 2.3%
E) 15.9%
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Fall Semester Final Exam 2012 Review #1
___ 15. Finish times (to the nearest hour) for 10 dogsled teams are shown below.
Find the class width. Use five classes. (Round your answer to the nearest integer.)
336
325
315
321
259
343
239
256
309
A) 116
B) 23
C) 118
D) 21
E) 22
266
___ 16. How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let
y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the
following information.
x 4
7
14
19
21
y 50 85 130 160 175
Would you say the correlation is low, moderate, or strong? Positive or negative? If necessary, draw a
scatter diagram of the given data.
A) strong and positive
B) moderate and positive
C) low and positive
D) strong and negative
E) moderate and negative
___ 17. Assume that x has a normal distribution, with the specified mean and standard deviation. Find the
indicated probabilities.
P ( 7 ≤ x ≤ 21) ; μ = 17; σ = 5
A)
B)
C)
D)
E)
0.212
0.115
0.788
0.765
0.023
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Fall Semester Final Exam 2012 Review #1
___ 18. Finish times (to the nearest hour) for 10 dogsled teams are shown below.
Make a frequency table showing class limits, class boundaries, midpoints, frequency, relative
frequencies, and cumulative frequencies. Use three classes. The class size of the given data is 24.
(Round your answer for relative frequency to the nearest hundredth and for midpoint to the nearest
tenth.)
257
308
262
310
268
299
249
286
239
278
Midpoint Freq. Relative
Cumulative
A) Class Limits Boundaries
Freq.
Freq.
236 − 260
235.5 − 260.5 248
3
0.3
3
261 − 284
260.5 − 284.5 273
3
0.3
6
285 − 308
284.5 − 308.5 297
4
0.4
10
B)
Class Limits Boundaries
Midpoint
236 − 260
261 − 285
286 − 310
248
273
298
235.5 − 260.5
260.5 − 285.5
285.5 − 310.5
C) Class Limits Boundaries
236 − 260
261 − 284
285 − 310
235.5 − 260.5
260.5 − 285.5
285.5 − 310.5
D) Class Limits Boundaries
236 − 260
261 − 284
285 − 308
235.5 − 260.5
260.5 − 284.5
284.5 − 308.5
Midpoint
248
273
297
Midpoint
248
273
297
Freq. Relative
Freq.
3
0.3
3
0.3
4
0.4
Cumulative
Freq.
3
6
10
Freq. Relative
Freq.
4
0.3
5
0.3
5
0.4
Cumulative
Freq.
3
6
10
Freq. Relative
Freq.
4
0.3
5
0.3
5
0.4
Cumulative
Freq.
3
6
10
E) none of theses choices
___ 19. Look at the normal curve given below, and find μ .
A)
B)
C)
D)
E)
μ = 22
μ=4
μ = 13
μ =3
μ = 16
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Fall Semester Final Exam 2012 Review #1
___ 20. You draw two cards from a standard deck of 52 cards and replace the first one before drawing the
second. Find the probability of drawing a 6 for the first card and a 2 for the second card. Round your
answer to the nearest thousandth.
A) 0.006
B) 0.039
C) 0.019
D) 0.155
E) 0.023
___ 21. At Center Hospital there is some concern about the high turnover of nurses. A survey was done to
determine how long (in months) nurses had been in their current positions. The responses (in
months) of 20 nurses were
23 2
5
14
25 36 27 42 12 8
7
12 29 26
28 11 20 31 8 36
Find the interquartile range.
A) 37.5
B) 19.0
C) 22.5
D) 38.0
E) 19.5
___ 22. Consider the data that was obtained from a random sample of 51 credit card accounts. Identify all
the averages (mean, median, or mode) that can be used to summarize the outstanding balance on
each account.
A) only mean and median if it exists
B) only mode and median if it exists
C) only mean and mode if it exists
D) mean, median, and mode if it exists
E) only median if it exists
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Fall Semester Final Exam 2012 Review #1
___ 23. Assume that the U.S Open Golf Tournament was played at Congressional Country club, with prizes
ranging from $ 465,000 for first place to $ 5000. Par for the course is 70. The tournament consists of
four rounds played on different days. Suppose the scores for each round of the 32 players who
placed in the money (more than $ 17,000) were given on a web site. The scores for the first round
were as follows:
76
71
66
65
75
75
75
71
72
73
72
70
74
71
71
73
70
72
71
72
72
71
71
73
74
71
71
73
74
67
70
70
70
72
74
70
67
The scores for the fourth round for these players were as follows:
68
69
67
74
72
72
67
73
72
71
71
70
74
72
70
66
69
70
Compare the two distributions.
A) Scores are equal for both the rounds.
B) Scores are lower in the first round.
C) Scores are lower in the fourth round.
D) none of these choices
70
65
69
71
70
71
71
71
73
___ 24. Data may be classified by one of the four levels of measurement. What is the name of the lowest
level?
A) interval
B) nominal
C) ordinal
D) ratio
E) simple
___ 25. Does the diagram below show a high linear correlation, a moderate or low linear correlation, or no
linear correlation?
A) moderate or low linear correlation
B) high linear correlation
C) no linear correlation
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Fall Semester Final Exam 2012 Review #1
___ 26. If event A is certain to occur, what is P(A)?
A) 0
B) 0.25
C) 0.5
D) 0.75
E) 1
___ 27. Plain candies come in various colors. Assume that the distribution of colors for plain candies is as
follows:
Color Purpl Yello Red Orang Green Blue Brown
e
w
e
Percent 18% 17%
18% 10%
7%
10% 20%
Suppose you have a large bag of plain candies and you take one candy at random. Find the
probability that the candy is either brown or orange. Round your answer to the nearest hundredth.
A) 0.02
B) 0.43
C) 0.29
D) 0.30
E) none of these choices
___ 28. Let z be a random variable with a standard normal distribution. Find the indicated probability below.
P ( z ≤ 0.9 )
A)
B)
C)
D)
E)
0.184
0.816
0.092
0.908
0.061
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Fall Semester Final Exam 2012 Review #1
___ 29. When do creative people get their good ideas? Assume that the survey of 963 inventors gives the
following information:
Time of Day When good Ideas Occur
Time
Number of Inventors
6 A.M. − 12 noon
290
12 noon − 6 P.M.
121
6 P.M. − 12 midnight
324
228
12 midnight − 6 A.M.
Assuming that the time interval includes the left limit and all the times up to but not including the
right limit, estimate the probability that an inventor has a good idea during the time interval from 6
A.M. to 12 noon. Write your answer as a fraction in simplest form.
1
A)
2
1
B)
4
290
C)
963
290
D)
673
E) none of these choices
___ 30. Are customers more loyal in the East or in the West? The following table is based on information
from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The
columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the
United Sates.
Less
1 − 2 3 − 4 5 − 9 10 − 14 15 or More
Row
Than 1
Years Years Years
Years
Years
Total
Year
East
32
54
59
112
77
118
452
Midwest
31
68
68
120
63
173
523
South
53
92
93
158
106
158
660
West
41
56
67
78
45
86
373
Column
157
270
287
468
291
535
2008
Total
What is the probability that a customer chosen at random is either from the East or from the West
given that he or she has been loyal less than 1 year? Round your answer to the nearest thousandth.
A) 0.088
B) 0.036
C) 0.417
D) 0.465
E) none of these choices
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Fall Semester Final Exam 2012 Review #1
___ 31. The qualified applicant pool for three management trainee positions consists of eight men and eight
women. How many different groups of trainees would consist entirely of women?
A) 2
B) 24
C) 56
D) 1
E) none of these choices
___ 32. How hot does it get in Death Valley? Assume that the following data are taken from a study
conducted by the National Park System, of which Death Valley is a unit. The ground temperatures
( D F ) were taken from May to November in the vicinity of Furnace Creek. Compute the median for
these ground temperatures. Round your answer to the nearest tenth.
150
152
169
175
196
178
187
196
178
178
169
163
152
145
A) 160.5
B) 169.0
C) 191.5
D) 344.0
E) 172.0
___ 33. Suppose automobile insurance companies gave annual premiums for top-rated companies in several
states. The figure below shows box plots for the annual premium for urban customers in three states.
Which state has the highest median premium?
A) Pennsylvania has the highest median premium.
B) Texas has the highest median premium.
C) Texas as well as California have the highest median premium.
D) California has the highest median premium.
E) none of these choices
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Fall Semester Final Exam 2012 Review #1
___ 34. The college hiking club is having a fund raiser to buy new equipment for fall and winter outings.
The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece
of paper with a different number written on it. A random drawing will determine which number is
the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $37. Since
fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 719
cookies before the drawing. Lisa bought 31 cookies. What is the probability she will win the dinner
for two? Write your answer as a fraction in simplest form, if one exists.
31
A)
688
688
B)
719
31
C)
719
1
D)
31
E) none of these choices
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Fall Semester Final Exam 2012 Review #1
___ 35. Shade the area under the standard normal curve corresponding to the probability below.
P ( –1 ≤ z ≤ 0 )
A)
B)
C)
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Fall Semester Final Exam 2012 Review #1
D)
E)
___ 36. The Grand Canyon and the Colorado River are beautiful, Rugged, and sometimes dangerous.
Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has
recorded (for a 5-year period) the number of visitor injuries at different landing points for
commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon.
Compare the mean, median, and mode found in Upper Canyon and Lower Canyon, respectively.
Upper Canyon: Number of injuries per Landing Point Between
North Canyon and Phantom Ranch
3 4 2 2 4 5 6 9 4 2 4
Lower Canyon: Number of injuries per Landing Point Between
Bright Angel and Lava Falls
8 2 2 0 6 7 3 11 4 0 2 10 3 2
A) Upper Canyon mean is greater than Lower Canyon, Upper Canyon median is greater than
Lower Canyon, and Upper Canyon mode is greater than Lower Canyon.
B) Upper Canyon mean is smaller than Lower Canyon, Upper Canyon median is smaller than
Lower Canyon, and Upper Canyon mode is greater than Lower Canyon.
C) Upper Canyon mean is smaller than Lower Canyon, Upper Canyon median is greater than
Lower Canyon, and Upper Canyon mode is smaller than Lower Canyon.
D) Upper Canyon mean is smaller than Lower Canyon, Upper Canyon median is greater than
Lower Canyon, and Upper Canyon mode is greater than Lower Canyon.
E) Upper Canyon mean is smaller than Lower Canyon, Upper Canyon median is smaller than
Lower Canyon, and Upper Canyon mode is smaller than Lower Canyon.
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Fall Semester Final Exam 2012 Review #1
___ 37. How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let
y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the
following information. Given the scatter diagram and "best fit" line for the data below, would you
say the correlation is low, moderate, or strong? Positive or negative?
A)
B)
C)
D)
E)
strong and positive
low and positive
moderate and negative
low and negative
strong and negative
___ 38. Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the
director of an insurance adjustment office. Your office has just received 132 insurance claims to be
processed in the next few days. What is the probability that from 31 to 37 of the claims have been
padded?
A) 0.346
B) 0.303
C) 0.236
D) 0.283
E) 0.311
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Fall Semester Final Exam 2012 Review #1
___ 39. Can a low barometer reading be used to predict maximum wind speed of an approaching tropical
cyclone? Let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the
maximum wind speed (in miles per hour) of the cyclone. Suppose a random sample of cyclones gave
the following information.
x 1014 935 980 955 995
y 50
80
60
135 84
Make a scatter diagram for the data.
A)
B)
C)
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Fall Semester Final Exam 2012 Review #1
D)
E)
___ 40. Richard has been given a 9-question multiple-choice quiz in his history class. Each question has
three answers, of which only one is correct. Since Richard has not attended the class recently, he
doesn't know any of the answers. Assuming that Richard guesses on all 9 questions, find the
probability that he will answer at least 3 questions correctly? Round your answer to the nearest
thousandth.
A) 0.273
B) 0.623
C) 0.333
D) 0.111
E) 0.500
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Fall Semester Final Exam 2012 Review #1
Answer Key
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D
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