Download Math1342: Statistics: Final Review

Math1342: Statistics: Final Review
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
1) You roll a six-sided die. Event B is rolling an even number.
1)
A) 3; Simple event because the die is only rolled once.
B) 2; Not a simple event because it is an event that consists of more than a single outcome.
C) 1; Simple event because it is an event that consists of a single outcome.
D) 3; Not a simple event because it is an event that consists of more than a single outcome.
2) You randomly select a computer from a batch of 50 which contains 3 defective computers. Event B
is selecting a defective computer.
A) 1; Simple event because it is an event that consists of only one type of computer.
B) 50; Not a simple event because it is an event that consists of more than a single outcome.
C) 3; Simple event because it is an event that consists of only one type of computer.
D) 3; Not a simple event because it is an event that consists of more than a single outcome.
From the information provided, create the sample space of possible outcomes.
3) Flip a coin twice.
A) HH HT TH TT
B) HH TT HT HT
C) HH HT TT
Determine whether the events are disjoint.
4) Draw one ball colored red from a bag.
Draw one ball colored blue from the same bag.
A) Yes
2)
3)
D) HT TH
4)
B) No
Find the indicated complement.
5) The probability that Luis will pass his statistics test is 0.26. Find the probability that he will fail his
statistics test.
A) 0.35
B) 0.74
C) 3.85
D) 0.13
6) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore
leap years.
11
31
334
31
A)
B)
C)
D)
12
365
365
334
Find the indicated probability.
7) If you pick a card at random from a well shuffled deck, what is the probability that you get a face
card or a spade?
1
25
11
9
A)
B)
C)
D)
22
52
26
26
1
5)
6)
7)
8) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 9 wood
and 14 graphite are defective and one racket is randomly selected from the sample, find the
probability that the racket is wood or defective.
A) 0.545
B) 0.115
C) 0.57
D) There is insufficient information to answer the question.
8)
9) 100 employees of a company are asked how they get to work and whether they work full time or
part time. The figure below shows the results. If one of the 100 employees is randomly selected,
find the probability of getting someone who carpools or someone who works full time.
9)
1. Public transportation: 8 full time, 6 part time
2. Bicycle: 4 full time, 3 part time
3. Drive alone: 29 full time, 32 part time
4. Carpool: 8 full time, 10 part time
A) 0.59
B) 0.67
10) A 6-sided die is rolled. Find P(3 or 5).
1
A)
B) 2
3
C) 0.28
D) 0.51
1
C)
36
1
D)
6
10)
11) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).
2
4
13
A)
B) 8
C)
D)
13
13
2
11)
12) A bag contains 6 red marbles, 2 blue marbles, and 1 green marble. Find P(not blue).
7
2
9
A)
B) 7
C)
D)
9
9
7
12)
13) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
351
47
70
48
516
Women
395
40
87
43
565
Total
746
87
157
91
1081
13)
If one of the 1081 people is randomly selected, find the probability of getting a regular or heavy
smoker.
A) 0.476
B) 0.229
C) 0.109
D) 0.145
2
14) In one town, 20% of all voters are Democrats. If two voters are randomly selected for a survey, find
the probability that they are both Democrats. Round to the nearest thousandth if necessary.
A) 0.038
B) 0.200
C) 0.040
D) 0.400
14)
15) When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of
dice are rolled 5 times, what is the probability of getting a sum of 5 every time? Round to eight
decimal places.
A) 0.00032
B) 0.04
C) 0.00001694
D) 0.00005168
15)
16) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing
cards. Find the probability that both cards are black. Express your answer as a simplified fraction.
13
1
25
25
A)
B)
C)
D)
51
2,652
102
51
16)
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
17) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
17)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years
of age given that they drink root beer.
6
2
A)
B)
17
5
C)
5
17
D) None of the above is correct.
Evaluate the expression.
12!
18)
7!
A) 2!
18)
B)
12
7
C) 95,040
D) 84,000
19) 5 P4
A) 24
B) 120
C) 1
D) 5
20) 8 C3
A) 112
B) 120
C) 56
D) 3
19)
20)
Solve the problem.
21) There are 13 members on a board of directors. If they must form a subcommittee of 5 members,
how many different subcommittees are possible?
A) 120
B) 1287
C) 154,440
D) 371,293
22) How many ways can an IRS auditor select 4 of 12 tax returns for an audit?
A) 20,736
B) 24
C) 11,880
3
21)
22)
D) 495
23) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is
not allowed?
A) 210
B) 6
C) 5
D) 343
23)
24) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to
choose from?
A) 48
B) 720
C) 20,160
D) 40,320
24)
25) In a certain lottery, five different numbers between 1 and 31 inclusive are drawn. These are the
winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order
in which they were drawn. What is the probability of winning?
120
1
1
1
A)
B)
C)
D)
20,389,320
120
31!
20,389,320
25)
Use the fundamental counting principle to solve the problem.
26) A shirt company has 4 designs each of which can be made with short or long sleeves. There are 7
color patterns available. How many different shirts are available from this company?
A) 28
B) 11
C) 13
D) 56
27) How many license plates can be made consisting of 2 letters followed by 3 digits?
A) 676,000
B) 67,600
C) 11,881,376
D) 100,000
Find the mean of the given probability distribution.
28) The number of golf balls ordered by customers of a pro shop has the following probability
distribution.
x P(x)
3 0.14
6 0.25
9 0.36
12 0.15
15 0.10
A) μ = 9
B) μ = 5.79
C) μ = 9.06
D) μ = 8.46
29) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a
given day are 0.48, 0.39, 0.12, and 0.01, respectively.
A) μ = 1.50
B) μ = 0.25
C) μ = 1.14
D) μ = 0.66
Provide an appropriate response. Round to the nearest hundredth.
30) Find the standard deviation for the given probability distribution.
x P(x)
0 0.12
1 0.17
2 0.09
3 0.28
4 0.34
A) σ = 2.91
B) σ = 1.99
C) σ = 1.41
4
26)
27)
28)
29)
30)
D) σ = 1.45
Provide an appropriate response.
31) In a game, you have a 1/27 probability of winning $100 and a 26/27 probability of losing $4. What is
your expected value?
A) -$3.85
B) $7.56
C) -$0.15
D) $3.70
32) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning
ticket is to be $500. What is your expected value?
A) -$0.50
B) -$1.00
C) $0.00
D) -$0.40
31)
32)
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.
1
33) n = 4, x = 3, p =
33)
6
A) 0.023
B) 0.015
C) 0.004
D) 0.012
Find the indicated probability. Round to three decimal places.
34) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions
correctly. If a student guesses on each question, what is the probability that the student will pass
the test?
A) 0.172
B) 0.377
C) 0.828
D) 0.205
Find the indicated probability.
35) An archer is able to hit the bull's-eye 50% of the time. If she shoots 8 arrows, what is the probability
that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
A) 0.00391
B) 0.219
C) 0.0625
D) 0.273
34)
35)
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
36) n = 2699; p = 0.63
36)
A) σ = 25.08
B) σ = 28.35
C) σ = 29.20
D) σ = 22.67
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
37) n = 671; p = 0.7
37)
A) μ = 471.0
B) μ = 468.2
C) μ = 469.7
D) μ = 471.4
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
38)
38)
-3.39 -2.26 -1.13
A) 0.8708
1.13
2.26
3.39
z
B) 0.8907
C) 0.8485
5
D) 0.1292
39)
39)
-2.95-2.36-1.77-1.18-0.59
z
0.59 1.18 1.77 2.36
A) 0.2776
B) 0.2190
C) 0.7224
D) 0.2224
40)
40)
-1.84
-0.92
A) 0.1788
0.92
1.84
z
B) 0.6424
C) 0.8212
D) 0.3576
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
41) Shaded area is 0.0901.
41)
z
A) -1.39
B) -1.34
C) -1.26
D) -1.45
42) Shaded area is 0.8599.
42)
z
A) 0.8051
B) 1.08
C) 0.5557
If z is a standard normal variable, find the probability.
43) The probability that z lies between 0 and 3.01
A) 0.1217
B) 0.9987
D) -1.08
43)
C) 0.4987
D) 0.5013
44) The probability that z lies between 0.7 and 1.98
A) -0.2181
B) 1.7341
C) 0.2175
D) 0.2181
45) P(z < 0.97)
A) 0.8315
C) 0.1660
D) 0.8078
44)
45)
B) 0.8340
6
Provide an appropriate response.
46) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of -1.645.
A) 91.0
B) 79.1
C) 82.3
D) 75.3
Provide an appropriate response. Use the Standard Normal Table to find the probability.
47) An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose less than 20 suitcases?
A) 0.8944
B) 0.4040
C) 0.1056
D) 0.3944
46)
47)
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread
evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of
pounds lost.
48) Between 8 pounds and 11 pounds
48)
2
1
1
1
A)
B)
C)
D)
3
3
4
2
Solve the problem.
49) The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean
weight will be between 8.6 and 14.6 lb?
A) 0.4032
B) 0.6730
C) 0.3270
D) 0.0968
49)
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
50) With n = 18 and p = 0.30, estimate P(6).
50)
A) 0.1015
B) 0.1958
C) 0.8513
D) 0.1239
51) A certain question on a test is answered correctly by 22% of the respondents. Estimate the
probability that among the next 150 responses there will be at most 40 correct answers.
A) 0.8997
B) 0.1003
C) 0.9306
D) 0.0694
51)
52) Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that
of 10,000 randomly selected hair dryers, at least 219 are defective.
A) 0.0934
B) 0.0869
C) 0.9066
D) 0.0823
52)
Use the normal distribution to approximate the desired probability.
53) Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives.
A) 0.5871
B) 0.8871
C) 0.6229
D) 0.7673
Find the percentile for the data value.
54) Data set: 6 6 21 18 6 15 27 27 33 9 6 27 18 3 27;
data value: 21
A) 60
B) 52
C) 70
54)
D) 35
Find the variance for the given data. Round your answer to one more decimal place than the original data.
55) 19 11 12 7 11
A) 18.9
B) 15.2
C) 19.0
D) 49.0
7
53)
55)
Find the number of standard deviations from the mean. Round your answer to two decimal places.
56) The test scores on the Chapter 7 mathematics test have a mean of 66 and a standard deviation of 13.
Andrea scored 89 on the test. How many standard deviations from the mean is that?
A) 0.60 standard deviations below the mean
B) 1.77 standard deviations below the mean
C) 1.77 standard deviations above the mean
D) 0.60 standard deviations above the mean
Provide an appropriate response.
57) 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) 40.5, 58.5
57)
Number of students
2
4
6
15
5
B) 40.5, 59.5
C) 39.5, 58.5
D) 39.5, 59.5
58) The frequency distribution below summarizes employee years of service for Alpha Corporation.
Determine the width of each class.
Years of service Frequency
1-5
5
6-10
20
11-15
25
16-20
10
21-25
5
26-30
3
A) 10
56)
B) 4
C) 5
8
D) 6
58)
59) The scores on a recent statistics test are given in the frequency distribution below. Construct the
corresponding relative frequency distribution. Round relative frequencies to the nearest hundredth
of a percent if necessary.
59)
Scores Frequency
0-60
4
61-70
9
71-80
10
81-90
5
91-100
5
A)
B)
Relative
Scores Frequency
0-60
12.5%
61-70
20.1%
71-80
37.3%
81-90
15.2%
91-100
14.9%
Relative
Scores Frequency
0-60
12.12%
61-70
27.27%
71-80
30.30%
81-90
15.15%
91-100 15.15%
C)
D)
Relative
Scores Frequency
0-60
15.5%
61-70
22.1%
71-80
31.3%
81-90
16.2%
91-100
14.9%
Relative
Scores Frequency
0-60
0.21%
61-70
0.18%
71-80
0.45%
81-90
0.06%
91-100
0.09%
60) The scores of the top ten finishers in a recent golf tournament are listed below. Find the median
score.
67 67 68
A) 72
71
72 72
72 72
60)
73 76
B) 67
C) 71
D) 73
61) The scores of the top ten finishers in a recent golf tournament are listed below. Find the mode
score.
61)
71 67 67 72 76 72 73 68 72 72
A) 72
B) 73
C) 76
Approximate the mean of the grouped data.
62)
Miles (per day) Frequency
1-2
29
3-4
12
5-6
18
7-8
2
9-10
16
A) 4
B) 5
D) 67
62)
C) 15
9
D) 6
Provide an appropriate response.
63) Find the sample standard deviation.
22
29 21 24
A) 1.6
27
28
63)
25 36
B) 4.8
C) 2.8
D) 4.2
Use the grouped data formulas to find the indicated mean or standard deviation.
64) The salaries of a random sample of a company's employees are summarized in the frequency
distribution below. Approximate the sample mean.
64)
Salary ($) Employees
5,001-10,000
14
10,001-15,000
16
15,001-20,000
14
20,001-25,000
17
25,001-30,000
19
A) $17,500
B) $20,006.80
C) $16,369.20
D) $18,188.00
Provide an appropriate response.
65) The ages of 10 grooms at their first marriage are listed below. Find the midquartile.
65)
35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9
A) 43.7
B) 34.1
C) 34.5
D) 34.2
66) A teacher gives a 20-point quiz to 10 students. The scores are listed below. What percentile
corresponds to the score of 12?
20 8 10 7 15 16 12 19 14 9
A) 25
B) 12
C) 40
D) 13
Find the number of standard deviations from the mean. Round your answer to two decimal places.
67) The test scores on the Chapter 4 mathematics test have a mean of 70 and a standard deviation of 13.
Andrea scored 92 on the test. How many standard deviations from the mean is that?
A) 1.69 standard deviations above the mean
B) 1.69 standard deviations below the mean
C) 0.62 standard deviations above the mean
D) 0.62 standard deviations below the mean
Find the percentile for the data value.
68) Data set: 20 20 70 40 20 50 90 90 110 30 20 90 60 10 90;
data value: 70
A) 70
B) 60
C) 35
67)
68)
D) 52
Find the number of standard deviations from the mean. Round your answer to two decimal places.
69) The test scores on the Chapter 2 mathematics test have a mean of 64 and a standard deviation of 14.
Andrea scored 93 on the test. How many standard deviations from the mean is that?
A) 0.54 standard deviations below the mean
B) 2.07 standard deviations above the mean
C) 0.54 standard deviations above the mean
D) 2.07 standard deviations below the mean
10
66)
69)
Solve the problem.
70) A sample of 51 eggs yields a mean weight of 1.58 ounces. Assuming that σ = 0.58 ounces, find the
margin of error in estimating μ at the 95% level of confidence.
A) 0.43 oz
B) 0.13 oz
C) 0.16 oz
D) 0.02 oz
Find the necessary sample size.
71) Scores on a certain test are normally distributed with a variance of 100. A researcher wishes to
estimate the mean score achieved by all adults on the test. Find the sample size needed to assure
with 95 percent confidence that the sample mean will not differ from the population mean by more
than 4 units.
A) 25
B) 2401
C) 97
D) 10
70)
71)
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of
decimal places as the sample mean unless otherwise noted.
72) Systolic blood pressures for women aged 18-24: 94% confidence; n = 96, x = 112.4 mm Hg,
σ = 12.7 mm Hg
A) 50.6 mm Hg
B) 2.4 mm Hg
C) 2.0 mm Hg
D) 2.2 mm Hg
Find the confidence interval specified.
73) A sample of 32 people were randomly selected from among the workers in a shoe factory. The time
taken for each person to polish a finished shoe was measured. The sample mean was 3.1 minutes.
Assume that σ = 0.94 minutes. Construct a 90% confidence interval for the true mean time, μ, to
polish a shoe.
A) 2.77 to 3.43 minutes
B) 2.71 to 3.49 minutes
C) 2.83 to 3.37 minutes
D) 2.67 to 3.53 minutes
72)
73)
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your
answer to the same number of decimal places as the sample mean.
74) Test scores: n = 104, x = 78.8, σ = 6.9; 99% confidence
A) 77.1 < μ < 80.5
B) 77.5 < μ < 80.1
74)
C) 77.2 < μ < 80.4
D) 77.7 < μ < 79.9
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
75) Margin of error: $139, confidence level: 95%, σ = $519
75)
A) 76
B) 38
C) 47
D) 54
A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the
required hypothesis test at the given significance level. Use the critical -value approach.
76) x = 20, n = 60, σ = 1.5, H0 : μ = 22; Ha : μ ≠ 22, α = 0.05
76)
A) z = -10.33; critical values = ±1.645; reject H0
B) z = -10.33; critical values = ±1.645; do not reject H0
C) z = -10.33; critical values = ±1.96; do not reject H0
D) z = -10.33; critical values = ±1.96; reject H0
77) x = 51, n = 52 , σ = 3.6, H0 : μ = 50; Ha : μ > 50, α = 0.01
A) z = 0.28; critical value = 2.33; do not reject H0
B) z = 2.00; critical value = 1.33; reject H0
C) z = 2.00; critical value = 2.33; reject H0
D) z = 2.00; critical value = 2.33; do not reject H0
11
77)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
78) The mean replacement time for a random sample of 20 washing machines is 9.2 years and the
78)
standard deviation is 2.0 years. Construct a 99% confidence interval for the standard deviation, σ,
of the replacement times of all washing machines of this type.
A) 1.4 yr < σ < 3.3 yr
B) 1.4 yr < σ < 3.8 yr
C) 1.4 yr < σ < 4.2 yr
D) 1.4 yr < σ < 3.2 yr
Provide an appropriate response.
79) Compute the standardized test statistic, X 2 to test the claim σ2 ≠ 13.6 if n = 10, s2 = 15, and α = 0.01.
A) 4.919
B) 9.926
C) 12.008
D) 3.276
Find the specified t-value.
80) For a t-curve with df = 6, find the two t-values that divide the area under the curve into a middle
0.99 area and two outside areas of 0.005.
A) -3.143, 3.143
B) 0, 3.143
C) 0, 3.707
D) -3.707, 3.707
79)
80)
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to
state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.
81) r = 0.41, n = 25
81)
A) Critical values: r = ±0.487, no significant linear correlation
B) Critical values: r = ±0.396, no significant linear correlation
C) Critical values: r = ±0.396, significant linear correlation
D) Critical values: r = ±0.487, significant linear correlation
Find the value of the linear correlation coefficient r.
82) x 46.2 21.9 25.6 47.9 39.0
y
10
4
5
2
5
A) 0.209
B) -0.209
82)
C) 0
D) 0.186
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if
necessary.
83) x 2 4 5 6
83)
y 7 11 13 20
^
A) y = 2.8x
^
^
B) y = 0.15 + 2.8x
C) y = 3.0x
12
^
D) y = 0.15 + 3.0x
Find the value of the chi-square test statistic for the goodness-of-fit test.
84) The following table is obtained from a random sample of 30 absences.
84)
Day
Mon Tue Wed Thur Fri
Number Absent
9
1
7
6
7
You wish to test the claim that the absences occur on the five days with equal frequency. What is
the value of the χ 2 test statistic? The observed frequencies and the expected frequencies are shown
below.
Observed
Expected
Frequency (O) Frequency (E)
9
6
1
6
7
6
6
6
7
6
2
2
A) χ = 9
B) χ = 3.6
C) χ 2 = 6
D) χ 2 = 4.5
Provide an appropriate response.
85) Many track runners believe that they have a better chance of winning if they start in the inside lane
that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is
Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track
runners in the different starting positions. Calculate the chi-square test statistic χ 2 to test the claim
that the number of wins is uniformly distributed across the different starting positions. The results
are based on 240 wins.
Starting Position
Number of Wins
A) 15.541
1 2 3 4 5 6
36 45 44 33 50 32
B) 6.750
C) 9.326
13
D) 12.592
85)
Answer Key
Testname: STATS-FINAL-REVIEW
1) D
2) D
3) A
4) A
5) B
6) C
7) C
8) C
9) A
10) A
11) A
12) A
13) B
14) C
15) C
16) C
17) B
18) C
19) B
20) C
21) B
22) D
23) A
24) C
25) D
26) D
27) A
28) D
29) D
30) C
31) C
32) A
33) B
34) B
35) D
36) A
37) C
38) A
39) A
40) B
41) B
42) D
43) C
44) D
45) B
46) D
47) A
48) D
49) B
50) B
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Answer Key
Testname: STATS-FINAL-REVIEW
51) C
52) A
53) D
54) A
55) C
56) C
57) D
58) C
59) B
60) A
61) A
62) B
63) B
64) D
65) D
66) C
67) A
68) B
69) B
70) C
71) A
72) B
73) C
74) A
75) D
76) D
77) D
78) A
79) B
80) D
81) C
82) A
83) C
84) C
85) B
15