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Ch 16, 17
Math 240 Exam 4 v2 Good SAMPLE
No Book, Yes 1 Page Notes, Yes Calculator, 120 Minutes
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the expected value of the random variable.
x
2
4 6
8
1)
P(X = x) 0.3 0.6 0.4 0.2
A) 7.4
B) 7
1)
C) 5
D) 6.6
E) 4
2) The number of golf balls ordered by customers of a pro shop has the following probability
distribution.
x
3
6
9 12 15
p(x) 0.14 0.08 0.36 0.32 0.10
A) 9.06
B) 6.81
C) 9
D) 8.04
1
E) 9.48
2)
Create a probability model for the random variable.
3) You roll a pair of fair dice. If you get a sum greater than 10 you win $70. If you get a double you
win $10. If you get a double and a sum greater than 10 you win $80. Otherwise you win nothing.
Create a probability model for the amount you win at this game.
Amount won
$0 $10 $70 $80
5
2
1
A) P(Amount won) 28
36
36
36
36
Amount won
$0
B) P(Amount won) 26
36
$10
6
36
$70
3
36
$80
1
36
Amount won
$10
5
36
$70
3
36
$80
1
36
Amount won
$10 $70
6
3
36 36
Amount won
$10
6
36
$0
C) P(Amount won) 27
36
$0
D) P(Amount won) 27
36
$0
E) P(Amount won) 27
36
$70
2
36
3)
$80
1
36
Find the expected value of the random variable.
4) A contractor is considering a sale that promises a profit of $23,000 with a probability of 0.7 or a loss
(due to bad weather, strikes, and such) of $9000 with a probability of 0.3. What is the expected
profit?
A) $18,800
B) $13,400
C) $16,100
2
D) $14,000
E) $22,400
4)
5) A company bids on two contracts. It anticipates a profit of $60,000 if it gets the larger contract and
a profit of $40,000 if it gets the smaller contract. It estimates that thereʹs a 10% chance of winning
the larger contract and a 50% chance of winning the smaller contract. Find the companyʹs expected
profit. Assume that the contracts will be awarded independently.
A) $21,000
B) $34,000
C) $31,000
D) $81,000
E) $26,000
Find the standard deviation of the random variable. Round to two decimal places if necessary.
x
3
6
9
12
6)
P(X = x) 0.1 0.4 0.3 0.2
A) 2.47
B) 7.82
C) 3.02
D) 2.20
3
5)
E) 2.75
6)
Create a probability model for the random variable.
7) A company is interviewing applicants for managerial positions. They plan to hire two people.
They have already rejected most candidates and are left with a group of 10 applicants of whom 3
are women. Unable to differentiate further between the applicants, they choose two people at
random from this group of 10.
Let the random variable X be the number of men that are chosen. Find the probability model for X.
0
1
2
A) Number men
P(Number men) 0.067 0.233 0.467
Number
men
0
1
2
B)
P(Number men) 0.090 0.420 0.490
0
1
2
C) Number men
P(Number men) 0.467 0.467 0.067
0
1
2
D) Number men
P(Number men) 0.067 0.467 0.467
0
1
2
E) Number men
P(Number men) 5.538 55.385 83.077
7)
Find the expected value of the random variable.
8) In a box of 10 batteries, 7 are dead. You choose two batteries at random from the box.
Let the random variable X be the number of good batteries you get. Find the expected value of X.
A) µ = 0.60
B) µ = 0.75
C) µ = 0.37
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D) µ = 0.82
E) µ = 1.40
8)
Find the standard deviation of the random variable.
9) You have arranged to go camping for two days in March. You believe that the probability that it
will rain on the first day is 0.3. If it rains on the first day, the probability that it also rains on the
second day is 0.6. If it doesnʹt rain on the first day, the probability that it rains on the second day is
0.3.
Let the random variable X be the number of rainy days during your camping trip. Find the
standard deviation of X.
A) σ = 0.75
B) σ = 0.76
C) σ = 0.67
D) σ = 0.65
9)
E) σ = 0.57
Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.
10) We record the blood types (O, A, B, or AB) found in a group of 300 people. Assume that the people
are unrelated to each other.
A) Yes.
B) No, 400 is more than 10% of the population.
C) No. More than two outcomes are possible.
D) No.The chance of getting a particular blood group changes from one person to the next.
E) No. The chance of getting a particular blood group depends on the blood groups already
recorded.
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10)
Find the indicated probability.
11) A basketball player has made 68% of his foul shots during the season. Assuming the shots are
independent, find the probability that in tonightʹs game he misses for the first time on his 9th
attempt?
A) 0.0457
B) 0.0099
C) 0.0146
D) 0.0311
E) 0.32
12) Suppose that in a certain population 45% of people have type O blood. A researcher selects
people at random from this population. What is the probability that there is a person with type O
blood among the first 6 people checked?
A) 0.0277
B) 0.9723
C) 0.0083
6
D) 0.0503
11)
E) 0.0226
12)
Solve.
13) An archer is able to hit the bullʹs eye 62% of the time. If she keeps shooting arrows until she hits the
bullʹs-eye, how long do you expect it will take? Assume each shot is independent of the others.
A) 2.63 shots
B) 0.62 shots
C) 1.61 shots
D) 62 shots
E) 0.38 shots
14) A company finds that 74% of applicants for a job do not have the required qualifications. How
many applications should they expect to read before finding a suitably qualified applicant?
A) 0.26
B) 1.35
C) 3.85
D) 0.74
13)
14)
E) 74
Find the indicated probability.
15) A multiple choice test has 8 questions each of which has 4 possible answers, only one of which is
correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability
that she will answer none of the questions correctly?
A) 0.1678
B) 0.0000153
C) 0.1001
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D) 0.9999847
E) 0.0250
15)
Find the probability of the outcome described.
16) A tennis player makes a successful first serve 52% of the time. If she serves 6 times, what is the
probability that she gets no more than 3 first serves in? Assume that each serve is independent of
the others.
A) 0.3820
B) 0.3070
C) 0.6180
D) 0.3110
16)
E) 0.6930
Find the indicated probability.
17) Police estimate that 65% of drivers wear their seat belts. If they stop 3 drivers at random, whatʹs
the probability that none of them are wearing their seat belts?
A) 0.105
B) 0.2746
C) 0.0429
D) 0.35
E) 0.195
18) A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in
tonightʹs game, what is the probability that he doesnʹt make all of the shots?
A) 0.657
B) 0.343
C) 0.09
D) 0.3
8
17)
E) 0.027
18)
Solve the problem.
19) A company manufactures batteries in batches of 14 and there is a 3% rate of defects. Find the mean
number of defects per batch.
A) 0.406
B) 3.0
C) 0.42
D) 13.58
E) 0.434
20) A company manufactures batteries in batches of 24 and there is a 3% rate of defects. Find the
standard deviation of the number of defects per batch.
A) 0.833
B) 0.818
C) 0.836
D) 0.849
19)
20)
E) 0.291
Describe an appropriate normal model that can be used to approximate the binomial distribution. If it is not appropriate
to use a normal approximation, give a reason why not.
21) A laboratory worker finds that 1.5% of his blood samples test positive for the HIV virus. If 265
blood samples are selected at random, is it appropriate to use a normal model to approximate the
distribution of the number that test positive for the HIV virus?
A) Yes; normal model with µ = 3.975 and σ = 1.98 can be used to approximate the distribution
B) No; normal model cannot be used to approximate the distribution because nq < 10
C) Yes; normal model with µ = 261.025 and σ = 1.98 can be used to approximate the distribution
D) Yes; normal model with µ = 3.975 and σ = 3.92 can be used to approximate the distribution
E) No; normal model cannot be used to approximate the distribution because np < 10
9
21)
Find the indicated probability by using an appropriate normal model to approximate the binomial distribution
22) In one city, police estimate that 78% of drivers wear their seat belts. They set up a safety roadblock
and they stop drivers to check for seat belt use. If 160 drivers are stopped, whatʹs the probability
they find at least 30 not wearing their seat belts?
A) 0.575
B) 0.161
C) 0.788
D) 0.839
22)
E) 0.425
Use a Poisson model to find the indicated probability.
23) On one tropical island, hurricanes occur with a mean of 2.32 per year. Assuming that the number
of hurricanes can be modeled by a Poisson distribution, find the probability that during the next 2
years the number of hurricanes will be 1.
A) 0.0224
B) 0.0448
C) 0.0983
D) 0.1040
E) 0.2280
24) The number of lightning strikes in a year at the top of a particular mountain has a Poisson
distribution with a mean of 3.8. Find the probability that in a randomly selected year, the number
of lightning strikes is 5.
A) 0.1477
B) 0.1920
C) 0.8523
10
D) 0.2511
23)
E) 0.0035
24)
Describe the indicated sampling distribution model.
25) Assume that 40% of students at a university wear contact lenses. We randomly pick 300 students.
Describe the sampling distribution model of the proportion of students in this group who wear
contact lenses.
25)
A) N(40%, 2.8%)
B) N(60%, 2.8%)
C) N(40%, 1.4%)
D) There is not enough information to describe the distribution.
E) Binom(300, 40)
Provide an appropriate response.
26) An archer is usually able to hit the bullʹs-eye 81% of the time. He buys a new bow hoping that it
will improve his success rate. During the first month of practice with his new bow he hits the
bullʹs-eye 415 times out of 500 shots. Is this evidence that with the new bow his success rate has
improved? In other words, is this an unusual result for him? Explain.
A) No; we would normally expect him to make 405 bullʹs-eyes with a standard deviation of
76.95. 415 is 0.1 standard deviations above the expected value. Thatʹs not an unusual result.
B) Yes; we would normally expect him to make 405 bullʹs-eyes with a standard deviation of
8.77. 415 is 1.1 standard deviations above the expected value. Thatʹs an unusual result.
C) No; we would normally expect him to make 405 bullʹs-eyes with a standard deviation of
20.12. 415 is 0.5 standard deviations above the expected value. Thatʹs not an unusual result.
D) Yes; we would normally expect him to make 405 bullʹs-eyes with a standard deviation of
76.95. 415 is 0.1 standard deviations above the expected value. Thatʹs an unusual result.
E) No; we would normally expect him to make 405 bullʹs-eyes with a standard deviation of
8.77. 415 is 1.1 standard deviations above the expected value. Thatʹs not an unusual result.
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26)
27) A multiple choice test consists of 60 questions. Each question has 4 possible answers only one of
which is correct. A student answers 26 questions correctly. Is that enough to convince you that he
is not merely guessing? Explain.
27)
A) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with
a standard deviation of 3.35. 26 is 3.3 standard deviations above the expected value. That
would be an unusual result.
B) No; if the student were guessing, we would expect him to answer 15 questions correctly with
a standard deviation of 3.35. 26 is 3.3 standard deviations above the expected value. That
would not be an unusual result.
C) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with
a standard deviation of 3.87. 26 is 2.8 standard deviations above the expected value. That
would be an unusual result
D) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with
a standard deviation of 3.10. 26 is 3.5 standard deviations above the expected value. That
would be an unusual result.
E) No; if the student were guessing, we would expect him to answer 15 questions correctly with
a standard deviation of 11.25. 26 is 0.98 standard deviations above the expected value. That
would not be an unusual result
Find the specified probability, from a table of Normal probabilities.
28) A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the
candies are packaged at random in small bags containing about 200 jelly beans. What is the
probability that a bag will contain more than 10% blue jelly beans?
A) 0.0239
B) 0.9227
C) 0.9544
12
D) 0.0478
E) 0.9761
28)
Find the indicated probability by using an appropriate normal model to approximate the binomial distribution
29) An archer is able to hit the bullʹs eye 76% of the time. If she shoots 160 arrows in a competition,
whatʹs the probability that she gets at least 130 bullʹs-eyes? Assume that shots are independent of
each other.
A) 0.939
B) 0.614
C) 0.061
D) 0.067
E) 0.386
30) A tennis player makes a successful first serve 65% of the time. If she serves 90 times in a match,
whatʹs the probability that she makes no more than 50 first serves? Assume that each serve is
independent of the others.
A) 0.663
B) 0.970
C) 0.030
D) 0.018
B) 0.121
C) 0.075
13
D) 0.081
30)
E) 0.337
31) An airline, believing that 6% of passengers fail to show up for flights, overbooks. Suppose a plane
will hold 320 passengers and the airline sells 335 seats. Whatʹs the probability the airline will not
have enough seats and will have to bump someone?
A) 0.375
29)
E) 0.919
31)
Answer Key
Testname: EXAM4V3 CH 16,17 V2 GOOD SAMPLE WITHBINOMIAL
1) B
2) E
3) A
4) B
5) E
6) E
7) D
8) A
9) B
10) C
11) C
12) B
13) C
14) C
15) C
16) C
17) C
18) A
19) C
20) C
21) E
22) D
23) B
24) A
25) A
26) E
27) A
28) E
29) C
30) C
31) D
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