Download STT 315 Practice Problems I for Sections 1.1 - 3.7.

STT 315 Practice Problems I for Sections 1.1 - 3.7.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Parking at a university has become a problem. University administrators are interested in
determining the average time it takes a student to find a parking spot. An administrator
inconspicuously followed 300 students and recorded how long it took each of them to find a
parking spot. Identify the variable of interest to the university administration.
A) number of empty parking spots
B) number of students who cannot find a spot
C) time to find a parking spot
D) students who drive cars on campus
1)
2) An assembly line is operating satisfactorily if fewer than 4% of the phones produced per day are
defective. To check the quality of a day's production, the company randomly samples 10 phones
from a day's production to test for defects. Define the population of interest to the manufacturer.
A) the 10 phones sampled and tested
B) the 4% of the phones that are defective
C) all the phones produced during the day in question
D) the 10 responses: defective or not defective
2)
3) The manager of a car dealership records the colors of automobiles on a used car lot. Identify the
type of data collected.
A) qualitative
B) quantitative
3)
4) An usher records the number of unoccupied seats in a movie theater during each viewing of a film.
Identify the type of data collected.
A) qualitative
B) quantitative
4)
5) What number is missing from the table?
5)
Year in
College
Freshman
Sophomore
Junior
Senior
A) 440
Frequency
600
560
400
Relative
Frequency
.30
.28
.22
.20
B) 520
C) 480
1
D) 220
6)
6)
The manager of a store conducted a customer survey to determine why customers shopped at the
store. The results are shown in the figure. What proportion of customers responded that
merchandise was the reason they shopped at the store?
2
1
3
A)
B)
C)
D) 30
7
2
7
7) A survey was conducted to determine how people feel about the quality of programming available
on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100
(extremely good quality). The stem-and-leaf display of the data is shown below.
Stem
3
4
5
6
7
8
9
7)
Leaf
8 9
0 3 4 7 8 9 9 9
0 1 1 2 3 4 5
1 2 5 6 6
2 4
3
What percentage of the respondents rated overall television quality as very good (regarded as
ratings of 80 and above)?
A) 3%
B) 4%
C) 1%
D) 12%
8) Fill in the blank. One advantage of the __________ is that the actual data values are retained in the
graphical summarization of the data.
A) stem-and-leaf plot
B) pie chart
C) histogram
2
8)
9) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify
for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens
were as follows:
67
73
68
62
59
72
60
91
67
86
65
88
75
80
74
75
64
61
69
63
9)
85
89
80
72
81
Find the median of the observations.
A) 73
B) 72.5
C) 69
D) 72
10) The scores for a statistics test are as follows:
10)
95 76 86 77 88 92 60 85 81 89
79 65 50 99 85 97 85 72 18 69
Compute the mean score.
A) 75
B) 77.40
C) 68.35
D) 80.60
11) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits
during the tournament. The statistician reported that the mean serve speed of a particular player
was 95 miles per hour. Suppose that the statistician indicated that the serve speed distribution was
skewed to the left. Which of the following values is most likely the value of the median serve
speed?
A) 104 mph
B) 77 mph
C) 86 mph
D) 95 mph
11)
12) A shoe company reports the mode for the shoe sizes of men's shoes is 12. Interpret this result.
A) Most men have shoe sizes between 11 and 13.
B) Half of all men's shoe sizes are size 12
C) Half of the shoes sold to men are larger than a size 12
D) The most frequently occurring shoe size for men is size 12
12)
13) Which of the following is not a measure of central tendency?
A) mode
B) mean
C) range
13)
D) median
14) Calculate the range of the following data set:
9, 5, 6, 3, 6, 14, 5, 5, 6
A) 14
14)
B) 11
C) 17
D) 3
15) The top speeds for a sample of five new automobiles are listed below. Calculate the standard
deviation of the speeds.
135, 180, 155, 170, 120
A) 241.5937
B) 24.6475
C) 171.6086
3
D) 139.59
15)
16) Each year advertisers spend billions of dollars purchasing commercial time on network television.
In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a
recent article, the top 10 leading spenders and how much each spent (in million of dollars) were
listed:
Company A $71.8
Company B 62.2
Company C 55.9
Company D 55.5
Company E 29.7
16)
Company F $25.9
Company G 25.7
Company H 21.5
Company I
21.4
Company J
20.8
Calculate the sample variance.
A) 1875.200
B) 394.907
C) 2092.713
D) 3781.844
17) Compute s2 and s for the data set: -2, -1, -3, -2, -1, -4
A) 32.63; 5.71
B) 0.2; 0.45
C) 0.24; 0.49
D) 1.37; 1.17
17)
18) The range of scores on a statistics test was 42. The lowest score was 57. What was the highest
score?
A) 70.5
B) cannot be determined
C) 78
D) 99
18)
19) Which of the following is a measure of the variability of a distribution?
A) median
B) sample size
C) range
19)
D) skewness
20) The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following
could be calculated using just this information?
A) median
B) standard deviation
C) range
D) variance
20)
Answer the question True or False.
21) A larger standard deviation means greater variability in the data.
A) True
B) False
21)
Solve the problem.
22) The total points scored by a basketball team for each game during its last season have been
summarized in the table below. Which statement following the table must be true?
22)
Score
41 -60
61 -80
81-100
101-120
Frequency
3
8
12
7
A) The range is at least 41 but at most 79.
C) The range is 79.
B) The range is at least 41 but at most 120.
D) The range is at least 81 but at most 100.
23) The mean x of a data set is 36.71, and the sample standard deviation s is 3.22. Find the interval
representing measurements within one standard deviation of the mean.
A) (35.71, 37.71)
B) (33.49, 39.93)
C) (27.05, 46.37)
D) (30.27, 43.15)
4
23)
24) The following is a list of 25 measurements:
12
13
12
18
14
16
14
11
17
17
16
19
18
16
15
14
13
18
17
15
15
24)
17
14
11
19
How many of the measurements fall within one standard deviation of the mean?
A) 13
B) 16
C) 25
D) 18
25) A standardized test has a mean score of 500 points with a standard deviation of 100 points. Five
students' scores are shown below.
Adam: 575
Beth: 690
Carlos: 750 Doug: 280
25)
Ella: 440
Which of the students have scores within two standard deviations of the mean?
A) Adam, Beth
B) Carlos, Doug
C) Adam, Beth, Carlos, Ella
D) Adam, Beth, Ella
26) A study was designed to investigate the effects of two variables (1) a student's level of
mathematical anxiety and (2) teaching method on a student's achievement in a mathematics
course. Students who had a low level of mathematical anxiety were taught using the traditional
expository method. These students obtained a mean score of 490 with a standard deviation of 40 on
a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage of
scores exceeded 410?
A) approximately 97.5%
B) approximately 95%
C) approximately 84%
D) approximately 100%
26)
27) A study was designed to investigate the effects of two variables (1) a student's level of
mathematical anxiety and (2) teaching method on a student's achievement in a mathematics
course. Students who had a low level of mathematical anxiety were taught using the traditional
expository method. These students obtained a mean score of 420 with a standard deviation of 20 on
a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would
approximately 99.7% of the students score?
A) below 480
B) below 360 and above 480
C) between 360 and 480
D) above 480
27)
28) A study was designed to investigate the effects of two variables (1) a student's level of
mathematical anxiety and (2) teaching method on a student's achievement in a mathematics
course. Students who had a low level of mathematical anxiety were taught using the traditional
expository method. These students obtained a mean score of 430 with a standard deviation of 20 on
a standardized test. Assuming no information concerning the shape of the distribution is known,
what percentage of the students scored between 390 and 470?
A) at least 75%
B) approximately 68%
C) at least 89%
D) approximately 95%
28)
5
29) By law, a box of cereal labeled as containing 20 ounces must contain at least 20 ounces of cereal.
The machine filling the boxes produces a distribution of fill weights with a mean equal to the
setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of
the boxes contain at least 20 ounces, the machine is set so that the mean fill per box is 20.09 ounces.
Assuming nothing is known about the shape of the distribution, what can be said about the
proportion of cereal boxes that contain less than 20 ounces.
A) The proportion is at most 11%.
B) The proportion is less than 2.5%.
C) The proportion is at most 5.5%.
D) The proportion is at least 89%.
29)
30) If nothing is known about the shape of a distribution, what percentage of the observations fall
within 2 standard deviations of the mean?
A) approximately 95%
B) at least 75%
C) at most 25%
D) approximately 5%
30)
31) Which of the following is a measure of relative standing?
A) mean
B) z-score
C) variance
31)
D) pie chart
32) Many firms use on-the-job training to teach their employees computer programming. Suppose
you work in the personnel department of a firm that just finished training a group of its employees
to program, and you have been requested to review the performance of one of the trainees on the
final test that was given to all trainees. The mean and standard deviation of the test scores are 79
and 2, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the
trainee in question received a score of 72. Compute the trainee's z-score.
A) z = -14
B) z = -7
C) z = 0.89
D) z = -3.50
32)
33) Summary information is given for the weights (in pounds) of 1000 randomly sampled tractor
trailers.
33)
MIN:
MAX:
AVE:
4005
10,605
7005
25%:
75%:
Std. Dev.:
5605
8605
1400
Find the percentage of tractor trailers with weights between 5605 and 8605 pounds.
A) 25%
B) 75%
C) 50%
D) 100%
34) When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated
with scores are also given. Suppose a test-taker scored at the 66th percentile on the verbal part of
the test and at the 45th percentile on the quantitative part. Interpret these results.
A) This student performed better than 34% of the other test-takers on the verbal part and better
than 55% on the quantitative part.
B) This student performed better than 66% of the other test-takers on the verbal part and better
than 55% on the quantitative part.
C) This student performed better than 34% of the other test-takers on the verbal part and better
than 45% on the quantitative part.
D) This student performed better than 66% of the other test-takers on the verbal part and better
than 45% on the quantitative part.
Answer the question True or False.
35) The mean of a data set is at the 50th percentile.
A) True
B) False
6
34)
35)
Solve the problem.
36) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits
during the tournament. The statistician reported that the mean serve speed of a particular player
was 102 miles per hour (mph) and the standard deviation of the serve speeds was 14 mph. Using
the z-score approach for detecting outliers, which of the following serve speeds would represent
outliers in the distribution of the player's serve speeds?
36)
Speeds: 53 mph, 116 mph, and 130 mph
A) 53, 116, and 130 are all outliers.
B) 53 is the only outlier.
C) 53 and 116 are both outliers, but 130 is not.
D) None of the three speeds is an outlier.
37) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too
high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured
senior citizens were as follows:
37)
68 73 66 76 86 74 61 89 65 90 69 92 76
62 81 63 68 81 70 73 60 87 75 64 82
Find the upper quartile of the data.
A) 92
B) 65.5
C) 73
D) 81.5
38) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits
during the tournament. The lower quartile of a particular player's serve speeds was reported to be
88 mph. Which of the following interpretations of this information is correct?
A) 75% of the player's serves were hit at speeds greater than 88 mph.
B) 88 serves traveled faster than the lower quartile.
C) 75% of the player's serves were hit at speeds less than 88 mph.
D) 25% of the player's serves were hit at 88 mph.
38)
39) The box plot shown below displays the amount of soda that was poured by a filling machine into
12-ounce soda cans at a local bottling company.
39)
Based on the box plot, what shape do you believe the distribution of the data to have?
A) skewed to the center
B) skewed to the right
C) approximately symmetric
D) skewed to the left
7
40) If sample points A, B, C, and D are the only possible outcomes of an experiment, find the
probability of D using the table below.
Sample Point
Probability
A)
A
1
8
3
8
B
1
8
B)
C
1
8
40)
D
5
8
C)
1
4
D)
1
8
41) The outcome of an experiment is the number of resulting heads when a nickel and a dime are
flipped simultaneously. What is the sample space for this experiment?
A) {HH, HT, TH, TT}
B) {0, 1, 2}
C) {HH, HT, TT}
D) {nickel, dime}
41)
42) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists
of randomly choosing one candy from the bag and recording its color. What is the sample space for
this experiment?
1 5 7
,
,
A)
B) {80}
4 16 16
42)
C) {red, yellow, orange}
D) {20, 25, 35}
43) An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that
the number chosen is even. List the sample points in E.
A) {2, 4, 6, 8, 10}
B) {1, 3, 5, 7, 9}
C) {5}
D) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
43)
44) Probabilities of different types of vehicle-to-vehicle accidents are shown below:
44)
Accident
Probability
Car to Car
0.65
Car to Truck
0.17
Truck to Truck 0.18
Find the probability that an accident involves a car.
A) 0.18
B) 0.17
C) 0.65
D) 0.82
45) At a community college with 500 students, 120 students are age 30 or older. Find the probability
that a randomly selected student is age 30 or older.
A) .76
B) .12
C) .24
D) .30
45)
46) A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50
miles of one of its physical stores. Using this estimate, what is the probability that a randomly
selected online customer does not live within 50 miles of a physical store?
A) .22
B) .28
C) .50
D) .78
46)
8
47) At a certain university, one out of every 20 students is enrolled in a statistics course. If one student
at the university is chosen at random, what is the probability that the student is enrolled in a
statistics course?
1
1
1
1
A)
B)
C)
D)
21
20
2
19
47)
48) Two chips are drawn at random and without replacement from a bag containing four blue chips
and three red chips. Find the probability of drawing two red chips.
1
6
9
1
A)
B)
C)
D)
7
7
49
12
48)
49) A pair of fair dice is tossed. Events A and B are defined as follows.
49)
A: {The sum of the numbers on the dice is 3}
B: {At least one of the dice shows a 2}
Identify the sample points in the event A B.
A) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)}
B) {(1, 2), (2, 1)}
C) {(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
D) {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
50) Consider the Venn diagram below where P(E1) = P(E2 ) =
1
1
P(E6 ) = P(E7 ) =
, and P(E8) = . Find P(A
20
5
A)
3
5
1
1
, P(E3) = P(E4) = P(E5 ) =
,
5
10
B).
B) 1
C)
9
1
2
D)
2
5
50)
51) Consider the Venn diagram below where P(E1) = 0.1, P(E2) = 0.2, P(E3 ) = 0.03, P(E4 ) = 0.06,
P(E5 ) = 0.06, P(E6 ) = 0.1, P(E7) = 0.06, P(E8 ) = 0.08, and P(E9) = 0.31. Find P(A
A) 1
B) 0.26
C) 0.69
51)
B).
D) 0.43
52) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the
state capital. Five hundred questionnaires were returned. Suppose an experiment consists of
randomly selecting one of the returned questionnaires. Consider the events:
52)
A: {The home is constructed of brick}
B: {The home is more than 30 years old}
In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years
old.
A) A Bc
B) A B
C) (A B)c
D) A B
53) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the
state capital. Five hundred questionnaires were returned. Suppose an experiment consists of
randomly selecting one of the returned questionnaires. Consider the events:
A: {The home is constructed of brick}
B: {The home is more than 30 years old}
D: {The home is heated with oil}
Which of the following describes the event B Dc?
A) homes that are not older than 30 years old and heated with oil
B) homes more than 30 years old that are heated with oil
C) homes more than 30 years old or homes that are not heated with oil
D) homes more than 30 years old that are not heated with oil
10
53)
54) Consider the Venn diagram below where P(E1) = 0.1, P(E2) = 0.2, P(E3 ) = 0.03, P(E4 ) = 0.04,
54)
P(E5 ) = 0.07, P(E6 ) = 0.1, P(E7) = 0.07, P(E8 ) = 0.07, and P(E9) = 0.32. Find P(Bc).
A) 0.66
B) 0.2
C) 0.56
D) 0.24
55) Consider the Venn diagram below where P(E1) = 0.1, P(E2) = 0.2, P(E3 ) = 0.05, P(E4 ) = 0.06,
P(E5 ) = 0.06, P(E6 ) = 0.1, P(E7) = 0.06, P(E8 ) = 0.03, and P(E9) = 0.34. Find P(Ac
A) 0.26
B) 0.78
C) 0.52
B).
D) 0.18
Answer the question True or False.
56) An event and its complement are mutually exclusive.
A) True
B) False
Solve the problem.
57) If P(A B) = 1 and P(A B) = 0, then which statement is true?
A) A and B are complementary events.
B) A and B are reciprocal events.
C) A and B are both empty events.
D) A and B are supplementary events.
Answer the question True or False.
58) If events A and B are not mutually exclusive, then it is possible that P(A) + P(B) > 1.
A) True
B) False
11
55)
56)
57)
58)
Solve the problem.
59) Suppose that for a certain experiment P(A) = .33 and P(B) = .29. If A and B are mutually exclusive
events, find P(A B).
A) .38
B) .62
C) .03
D) .31
60) Suppose that for a certain experiment P(A) = .47 and P(B) = .25 and P(A
A) .86
B) .36
C) .72
B) = .14. Find P(A B).
D) .58
61) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles
involved and whether alcohol played a role in the accident were recorded. The results are shown
below:
59)
60)
61)
Number of Vehicles Involved
Did Alcohol Play a Role?
1
2
3 or more Totals
Yes
53
95
22
170
No
30
174
26
230
Totals
83
269
48
400
Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident
involved alcohol or a single car?
17
1
53
83
A)
B)
C)
D)
40
2
400
400
62) In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an
A. If a student is randomly selected from the class, find the probability that the student is a woman
given that the student is earning an A.
11
7
7
5
A)
B)
C)
D)
20
22
10
11
62)
63) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles
involved and whether alcohol played a role in the accident were recorded. The results are shown
below:
63)
Number of Vehicles Involved
Did Alcohol Play a Role?
1
2
3 or more Totals
Yes
58
92
20
170
No
28
179
23
230
Totals
86
271
43
400
Given that an accident involved multiple vehicles, what is the probability that it involved alcohol?
20
7
1
56
A)
B)
C)
D)
43
25
20
157
64) For two events, A and B, P(A) = .4, P(B) = .7, and P(A
A) .29
B) .14
B) = .2. Find P(A | B).
C) .08
65) For two events, A and B, P(A) = .6, P(B) = .8, and P(A | B) = .5. Find P(A
A) .4
B) .3
C) .833
12
B).
D) .5
D) .625
64)
65)
66) Suppose that for a certain experiment P(B) = .5 and P(A B) = .2. Find P(A
A) .3
B) .1
C) .4
B).
D) .7
66)
67) Suppose that for a certain experiment P(A) = .6 and P(B) = .3. If A and B are independent events,
find P(A B).
A) .18
B) .90
C) .50
D) .30
67)
68) A study revealed that 45% of college freshmen are male and that 18% of male freshmen earned
college credits while still in high school. Find the probability that a randomly chosen college
freshman will be male and have earned college credits while still in high school.
A) .400
B) .081
C) .530
D) .027
68)
69) A number between 1 and 10, inclusive, is randomly chosen. Events A, B, C, and D are defined as
follows.
69)
A: {The number is even}
B: {The number is less than 7}
C: {The number is less than or equal to 7}
D: {The number is 5}
Identify one pair of independent events.
A) A and B
B) A and D
C) A and C
D) B and D
70) Classify the events as dependent or independent: Events A and B where P(A) = 0.2, P(B) = 0.1, and
P(A and B) = 0.02.
A) dependent
B) independent
70)
71) From 9 names on a list, a sample of 4 will be asked about voting preferences in an upcoming
election. How many different samples are possible?
A) 3024
B) 1512
C) 15,120
D) 126
71)
72) Which expression is equal to
A)
N!
(N - n)!
N
?
n
B)
72)
N!
N!(N - n)!
C)
N!
n!
D)
N!
n!(N - n)!
73) Kim submitted a list of 12 movies to an online movie rental company. The company will choose 3
of the movies and ship them to her. If all movies are equally likely to be chosen, what is the
probability that Kim will receive the three movies that she most wants to watch?
1
1
1
1
A)
B)
C)
D)
220
1728
1320
4
73)
74) Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and
74)
75) Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and
75)
P(B2 ) = .4. Consider another event A such that P(A | B1 ) = .2 and P(A | B2) = .5. Find P(A).
A) .32
B) .70
C) .88
D) .38
P(B2 ) = .4. Consider another event A such that P(A | B1 ) =.2 and P(A | B2) = .5. Find P(B1 | A).
A) .375
B) .800
C) .625
D) .240
13
76) 2.5% of a population are infected with a certain disease. There is a test for the disease, however the
test is not completely accurate. 94.9% of those who have the disease will test positive. However
4.5% of those who do not have the disease will also test positive (false positives). What is the
probability that a person who tests positive actually has the disease?
A) 0.025
B) 0.949
C) 0.649
D) 0.541
E) 0.351
76)
77) In the town of Maplewood a certain type of DVD player is sold at just two stores. 42% of the sales
are from store A and 58% of the sales are from store B. 2.3% of the DVD players sold at store A are
defective while 3.7% of the DVD players sold at store B are defective. If Kate receives one of these
DVD players as a gift and finds that it is defective, what is the probability that it came from store
A?
A) 0.023
B) 0.42
C) 0.690
D) 0.450
E) 0.310
77)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
78) For a given data set, the lower quartile is 45, the median is 50, and the upper quartile is 57.
The minimum value in the data set is 32, and the maximum is 81.
a.
b.
c.
d.
78)
Find the interquartile range.
Find the inner fences.
Find the outer fences.
Is either of the minimum or maximum values considered an outlier? Explain.
79) The calculator screens summarize a data set.
79)
a. Identify the lower and upper quartiles of the data set.
b. Find the interquartile range.
c. Is there reason to suspect that the data may contain an outlier? Explain.
80) Use a graphing calculator or software to construct a box plot for the following data set.
12
13
12
18
14
16
14
11
17
17
16
19
18
16
15
14
13
18
17
15
15
17
14
80)
11
19
81) Suppose that an experiment has five sample points, E1 , E2 , E3, E4, E5 , and that P(E1 ) = 0.2,
81)
82) Suppose that for a certain experiment P(A) = .37. Find P(Ac).
82)
P(E2 ) = 0.3, P(E3 ) = 0.1, P(E4 ) = 0.1, and P(E5) = 0.3. If the events A and B are defined as
A = {E1 , E2, E3 } and B = {E2 , E3, E4 }, find P(A B).
14
83) Two chips are drawn at random and without replacement from a bag containing two blue
chips and two red chips. Event A is defined as follows.
83)
A: {Both chips are red}
a.
b.
c.
Describe the event Ac.
Identify the sample points in the event Ac.
Find P(Ac).
84) Suppose there is a 36% chance that a risky stock investment will end up in a total loss of
your investment. Because the rewards are so high, you decide to invest in three
independent risky stocks. What is the probability that all three stocks end up in total
losses?
15
84)
STT 315 Practice Test 1 - ANSWERS
1) C
2) C
3) A
4) B
5) A
6) C
7) B
8) A
9) D
10) B
11) A
12) D
13) C
14) B
15) B
16) B
17) D
18) D
19) C
20) C
21) A
22) A
23) B
24) B
25) D
26) A
27) C
28) A
29) A
30) B
31) B
32) D
33) C
34) D
35) B
36) B
37) D
38) A
39) D
40) B
41) B
42) C
43) A
44) D
45) C
46) D
47) B
48) A
49) D
50) C
51) C
52) A
53) C
54) C
55) D
56) A
57) A
58) A
59) B
60) D
61) B
62) C
63) D
64) A
65) A
66) B
67) A
68) B
69) A
70) B
71) D
72) D
73) A
74) A
75) A
76) E
77) E
The interquartile range is 57 - 45 = 12.
The inner fences are 45 - 1.5(12) = 27 and 57 +
1.5(12) = 75.
c. The outer fences are 45 - 3(12) = 9 and 57 + 3(12)
= 93.
d. The maximum of 81 is a potential outlier since it
lies outside the inner fences. The minimum is within
the inner fence and is not considered to be an outlier.
79)
a. lower quartile: Q1=75; upper quartile: Q3=90
b. interquartile range: 90 - 75 = 15
c. Yes; the smallest measurement, 30, is three
times the interquartile range less than the lower
quartile, so it is a suspected outlier.
80) The horizontal axis extends from 10 to 20, with each
tick mark representing one unit.
78) a.
b.
81) A ∩ B = { ,
}; P(A ∩ B) = P(
c
82) P(A ) = 1 - 0.37 = .63
83)
84) Let
) + P(
a.
b.
At least one chip is not red.
{b1b2, b1r1, b1r2, b2r1, b2r2}
c.
P(Ac) =5/6
be the event that stock i ends up in a total loss.
P(all three stocks end in total loss) = P(
= P(
) = 0.3 + 0.1 = 0.4
) × P(
) × P(
∩
∩
) = 0.36 × 0.36 × 0.36 = 0.047
)