Download Probability Distributions

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) State whether the variable is discrete or continuous.
The number of cups of coffee sold in a cafeteria during lunch
A) discrete
B) continuous
2) State whether the variable is discrete or continuous.
The height of a player on a basketball team
A) discrete
3) State whether the variable is discrete or continuous.
The cost of a Statistics textbook
A) discrete
1)
2)
B) continuous
3)
B) continuous
4) State whether the variable is discrete or continuous.
The blood pressures of a group of students the day before their final exam
A) continuous
B) discrete
4)
5) State whether the variable is discrete or continuous.
The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
A) discrete
B) continuous
5)
6) State whether the variable is discrete or continuous.
The number of goals scored in a soccer game
A) discrete
6)
B) continuous
7) State whether the variable is discrete or continuous.
The speed of a car on a Los Angeles freeway during rush hour traffic
A) continuous
B) discrete
7)
8) State whether the variable is discrete or continuous.
The number of phone calls to the attendance office of a high school on any given school day
A) continuous
B) discrete
8)
9) State whether the variable is discrete or continuous.
The age of the oldest student in a statistics class
A) continuous
9)
10) State whether the variable is discrete or continuous.
The number of pills in a container of vitamins
A) discrete
B) discrete
10)
B) continuous
11) State whether the variable is discrete or continuous.
The number of cups of coffee sold in a cafeteria during lunch
A) continuous
B) discrete
1
11)
12) State whether the variable is discrete or continuous.
The height of a player on a basketball team
A) discrete
13) State whether the variable is discrete or continuous.
The cost of a Statistics textbook
A) continuous
12)
B) continuous
13)
B) discrete
14) State whether the variable is discrete or continuous.
The blood pressures of a group of students the day before their final exam
A) discrete
B) continuous
14)
15) State whether the variable is discrete or continuous.
The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
A) discrete
B) continuous
15)
16) State whether the variable is discrete or continuous.
The number of goals scored in a soccer game
A) continuous
16)
B) discrete
17) State whether the variable is discrete or continuous.
The speed of a car on a Los Angeles freeway during rush hour traffic
A) discrete
B) continuous
17)
18) State whether the variable is discrete or continuous.
The number of phone calls to the attendance office of a high school on any given school day
A) continuous
B) discrete
18)
19) State whether the variable is discrete or continuous.
The age of the oldest student in a statistics class
A) continuous
19)
20) State whether the variable is discrete or continuous.
The number of pills in a container of vitamins
A) continuous
B) discrete
20)
B) discrete
21) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has less than two cars.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.809
B) 0.125
C) 0.553
2
D) 0.428
21)
22) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has at least one car.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.500
B) 0.125
C) 0.083
D) 0.875
23) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has between one and three cars,
inclusive.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.208
B) 0.125
C) 0.792
22)
23)
D) 0.256
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
24) A student has five motor vehicle accidents in one year and claims that having five
accidents is not unusual. Use the frequency distribution below to determine if the student
is correct.
24)
Accidents 0 1 2 3 4 5
Students 260 500 425 305 175 45
25) A baseball player gets four hits during the World Series and a sports announcer claims
that getting four or more hits is not unusual. Use the frequency distribution below to
determine if the sports announcer is correct.
25)
Hits
0 1 2 3 4 5 6 7
Players 7 9 7 4 1 1 2 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
26) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has less than two cars.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.125
B) 0.553
C) 0.428
3
D) 0.809
26)
27) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has at least one car.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.875
B) 0.125
C) 0.083
D) 0.500
28) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has between one and three cars,
inclusive.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.208
B) 0.125
C) 0.256
D) 0.792
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
29) A student has five motor vehicle accidents in one year and claims that having five
accidents is not unusual. Use the frequency distribution below to determine if the student
is correct.
29)
Accidents 0 1 2 3 4 5
Students 260 500 425 305 175 45
30) A baseball player gets four hits during the World Series and a sports announcer claims
that getting four or more hits is not unusual. Use the frequency distribution below to
determine if the sports announcer is correct.
30)
Hits
0 1 2 3 4 5 6 7
Players 7 9 7 4 1 1 2 1
31) A sports analyst records the winners of NASCAR Winston Cup races for a recent season.
The random variable x represents the races won by a driver in one season. Use the
frequency distribution to construct a probability distribution.
Wins
1 2 3 4 5 6 7
Drivers 12 2 0 2 0 0 1
4
27)
31)
28)
32) An insurance actuary asked a sample of senior citizens the cause of their automobile
accidents over a two-year period. The random variable x represents the number of
accidents caused by their failure to yield the right of way. Use the frequency distribution
to construct a probability distribution.
32)
Accidents
0 1 2 3 4 5
Senior Citizens 4 3 12 3 2 1
33) A sports announcer researched the performance of baseball players in the World Series.
The random variable x represents the number of of hits a player had in the series. Use the
frequency distribution to construct a probability distribution.
33)
Hits
0 1 2 3 4 5 6 7
Players 7 9 7 4 1 1 2 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
34) Determine the probability distributionʹs missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
34)
x
0 1 2 3 4
1
2 2 1
? P(x) 21
7 21 7
A)
10
21
B)
3
7
C)
4
7
D) - 10
21
35)
35) Determine the probability distributionʹs missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
x
0
1
2
3 4
P(x) 0.03 0.39 0.07 0.36 ?
A) -0.57
B) 0.15
C) 0.58
D) 0.85
36) Determine the probability distributionsʹs missing value.
The probability that a tutor sees 0, 1, 2, 3, or 4 students on a given day.
x
0 1
2
3
4
P(x) ? 0.15 0.20 0.20 0.25
A) 0.50
B) 0.20
C) 1.0
36)
D) 0.80
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
37) The random variable x represents the number of boys in a family of three children.
Assuming that boys and girls are equally likely, (a) construct a probability distribution,
and (b) graph the distribution.
5
37)
38) The random variable x represents the number of tests that a patient entering a hospital
will have along with the corresponding probabilities. Graph the probability distribution.
38)
x
0 1 2 3 4
3 5 6 2 1
P(x)
17 17 17 17 17
39) The random variable x represents the number of credit cards that adults have along with
the corresponding probabilities. Graph the probability distribution.
39)
x P(x)
0 0.07
1 0.68
2 0.21
3 0.03
4 0.01
40) In a pizza takeout restaurant, the following probability distribution was obtained. The
random variable x represents the number of toppings for a large pizza. Graph the
probability distribution.
x
0
1
2
3
4
40)
P(x)
0.30
0.40
0.20
0.06
0.04
41) Use the frequency distribution to (a) construct a probability distribution for the random
variable x represents the number of cars per household in a town of 1000 households, and
(b) graph the distribution.
41)
Cars Households
0
125
1
428
2
256
3
108
4
83
42) A sports analyst records the winners of NASCAR Winston Cup races for a recent season.
The random variable x represents the races won by a driver in one season. Use the
frequency distribution to construct a probability distribution.
Wins
1 2 3 4 5 6 7
Drivers 12 2 0 2 0 0 1
6
42)
43) An insurance actuary asked a sample of senior citizens the cause of their automobile
accidents over a two-year period. The random variable x represents the number of
accidents caused by their failure to yield the right of way. Use the frequency distribution
to construct a probability distribution.
43)
Accidents
0 1 2 3 4 5
Senior Citizens 4 3 12 3 2 1
44) A sports announcer researched the performance of baseball players in the World Series.
The random variable x represents the number of of hits a player had in the series. Use the
frequency distribution to construct a probability distribution.
44)
Hits
0 1 2 3 4 5 6 7
Players 7 9 7 4 1 1 2 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
45) Determine the probability distributionʹs missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
45)
x
0
1
2 3 4
2
4
5
5
? P(x) 17
17 17 17
A)
1
17
B) - 10
17
C)
2
17
D)
16
17
46)
46) Determine the probability distributionʹs missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
x
0
1
2
3 4
P(x) 0.57 0.07 0.16 0.02 ?
A) 0.82
B) -0.82
C) 0.36
D) 0.18
47) Determine the probability distributionsʹs missing value.
The probability that a tutor sees 0, 1, 2, 3, or 4 students on a given day.
x
0 1
2
3
4
P(x) ? 0.15 0.20 0.20 0.25
A) 1.0
B) 0.20
C) 0.80
47)
D) 0.50
48) The random variable x represents the number of boys in a family of three children. Assuming that
boys and girls are equally likely, find the mean and standard deviation for the random variable x.
A) mean: 1.50; standard deviation: 0.76
B) mean: 1.50; standard deviation: 0.87
C) mean: 2.25; standard deviation: 0.87
D) mean: 2.25; standard deviation: 0.76
7
48)
49) The random variable x represents the number of tests that a patient entering a hospital will have
along with the corresponding probabilities. Find the mean and standard deviation.
49)
x
0 1 2 3 4
3 5 6 2 1
P(x)
17 17 17 17 17
A) mean: 1.59; standard deviation: 3.71
C) mean: 2.52; standard deviation: 1.93
B) mean: 1.59; standard deviation: 1.09
D) mean: 3.72; standard deviation: 2.52
50) The random variable x represents the number of credit cards that adults have along with the
corresponding probabilities. Find the mean and standard deviation.
50)
x P(x)
0 0.07
1 0.68
2 0.21
3 0.03
4 0.01
A) mean: 1.30; standard deviation: 0.44
C) mean: 1.23; standard deviation: 0.44
B) mean: 1.30; standard deviation: 0.32
D) mean: 1.23; standard deviation: 0.66
51) In a pizza takeout restaurant, the following probability distribution was obtained. The random
variable x represents the number of toppings for a large pizza. Find the mean and standard
deviation.
x
0
1
2
3
4
P(x)
0.30
0.40
0.20
0.06
0.04
A) mean: 1.30; standard deviation: 2.38
C) mean: 1.14; standard deviation: 1.04
51)
B) mean: 1.54; standard deviation: 1.30
D) mean: 1.30; standard deviation: 1.54
52) One thousand tickets are sold at $4 each. One ticket will be randomly selected and the winner will
receive a color television valued at $350. What is the expected value for a person that buys one
ticket?
A) $1.00
B) $3.65
C) -$1.00
D) -$3.65
52)
53) If a person rolls doubles when tossing two dice, the roller profits $75. If the game is fair, how much
should the person pay to play the game?
A) $75
B) $15
C) $72
D) $74
53)
54) At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and $400.
What is the expected value of one ticket?
A) $0.64
B) $4.36
C) -$4.36
D) -$0.64
54)
55) At a raffle, 10,000 tickets are sold at $10 each for three prizes valued at $4,800, $1,200, and $400.
What is the expected value of one ticket?
A) -$0.64
B) -$9.36
C) $0.64
D) $9.36
55)
8
56) In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner
will receive a laptop computer valued at $1200. What is the expected value for a person that buys
one ticket?
A) -$1.20
B) $1.20
C) $0.8
D) -$0.80
56)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
57) From the probability distribution, find the mean and standard deviation for the random
variable x, which represents the number of cars per household in a town of 1000
households.
x
0
1
2
3
4
57)
P(x)
0.125
0.428
0.256
0.108
0.083
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
58) The random variable x represents the number of boys in a family of three children. Assuming that
boys and girls are equally likely, find the mean and standard deviation for the random variable x.
A) mean: 2.25; standard deviation: 0.76
B) mean: 1.50; standard deviation: 0.87
C) mean: 1.50; standard deviation: 0.76
D) mean: 2.25; standard deviation: 0.87
58)
59) The random variable x represents the number of tests that a patient entering a hospital will have
along with the corresponding probabilities. Find the mean and standard deviation.
59)
x
0 1 2 3 4
3 5 6 2 1
P(x)
17 17 17 17 17
A) mean: 2.52; standard deviation: 1.93
C) mean: 1.59; standard deviation: 3.71
B) mean: 1.59; standard deviation: 1.09
D) mean: 3.72; standard deviation: 2.52
60) The random variable x represents the number of credit cards that adults have along with the
corresponding probabilities. Find the mean and standard deviation.
x P(x)
0 0.07
1 0.68
2 0.21
3 0.03
4 0.01
A) mean: 1.30; standard deviation: 0.44
C) mean: 1.23; standard deviation: 0.66
B) mean: 1.23; standard deviation: 0.44
D) mean: 1.30; standard deviation: 0.32
9
60)
61) In a pizza takeout restaurant, the following probability distribution was obtained. The random
variable x represents the number of toppings for a large pizza. Find the mean and standard
deviation.
x
0
1
2
3
4
P(x)
0.30
0.40
0.20
0.06
0.04
A) mean: 1.14; standard deviation: 1.04
C) mean: 1.30; standard deviation: 1.54
61)
B) mean: 1.30; standard deviation: 2.38
D) mean: 1.54; standard deviation: 1.30
62) One thousand tickets are sold at $2 each. One ticket will be randomly selected and the winner will
receive a color television valued at $350. What is the expected value for a person that buys one
ticket?
A) -$1.00
B) $1.00
C) $1.65
D) -$1.65
62)
63) If a person rolls doubles when tossing two dice, the roller profits $95. If the game is fair, how much
should the person pay to play the game?
A) $95
B) $94
C) $19
D) $92
63)
64) At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and $400.
What is the expected value of one ticket?
A) $4.36
B) -$0.64
C) $0.64
D) -$4.36
64)
65) At a raffle, 10,000 tickets are sold at $10 each for three prizes valued at $4,800, $1,200, and $400.
What is the expected value of one ticket?
A) -$0.64
B) -$9.36
C) $0.64
D) $9.36
65)
66) In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner
will receive a laptop computer valued at $1200. What is the expected value for a person that buys
one ticket?
A) -$0.80
B) -$1.20
C) $1.20
D) $0.8
66)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
67) From the probability distribution, find the mean and standard deviation for the random
variable x, which represents the number of cars per household in a town of 1000
households.
x
0
1
2
3
4
67)
P(x)
0.125
0.428
0.256
0.108
0.083
68) Decide whether the experiment is a binomial experiment. If it is not, explain why. You
observe the gender of the next 700 babies born at a local hospital. The random variable
represents the number of girls.
10
68)
69) Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll
a die 350 times. The random variable represents the number that appears on each roll of
the die.
69)
70) Decide whether the experiment is a binomial experiment. If it is not, explain why. You
spin a number wheel that has 20 numbers 450 times. The random variable represents the
winning numbers on each spin of the wheel.
70)
71) Decide whether the experiment is a binomial experiment. If it is not, explain why. You test
four pain relievers. The random variable represents the pain reliever that is most effective.
71)
72) Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing
a pain reliever using 80 people to determine if it is effective. The random variable
represents the number of people who find the pain reliever to be effective.
72)
73) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Surveying 1000 prisoners to see how many crimes in which they were convicted. The
random variable represents the number of crimes in which each prisoner was convicted.
73)
74) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Surveying 850 prisoners to see whether they are serving time for their first offense. The
random variable represents the number of prisoners serving time for their first offense.
74)
75) Decide whether the experiment is a binomial experiment. If it is not, explain why. Each
week, a man plays a game in which he has a 41% chance of winning. The random variable
is the number of times he wins in 49 weeks.
75)
76) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Selecting five cards, one at a time without replacement, from a standard deck of cards. The
random variable is the number of red cards obtained.
76)
77) Decide whether the experiment is a binomial experiment. If it is not, explain why. You
observe the gender of the next 300 babies born at a local hospital. The random variable
represents the number of girls.
77)
78) Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll
a die 650 times. The random variable represents the number that appears on each roll of
the die.
78)
79) Decide whether the experiment is a binomial experiment. If it is not, explain why. You
spin a number wheel that has 17 numbers 250 times. The random variable represents the
winning numbers on each spin of the wheel.
79)
80) Decide whether the experiment is a binomial experiment. If it is not, explain why. You test
four pain relievers. The random variable represents the pain reliever that is most effective.
80)
81) Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing
a pain reliever using 840 people to determine if it is effective. The random variable
represents the number of people who find the pain reliever to be effective.
81)
11
82) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Surveying 100 prisoners to see how many crimes in which they were convicted. The
random variable represents the number of crimes in which each prisoner was convicted.
82)
83) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Surveying 550 prisoners to see whether they are serving time for their first offense. The
random variable represents the number of prisoners serving time for their first offense.
83)
84) Decide whether the experiment is a binomial experiment. If it is not, explain why. Each
week, a man plays a game in which he has a 26% chance of winning. The random variable
is the number of times he wins in 50 weeks.
84)
85) Decide whether the experiment is a binomial experiment. If it is not, explain why.
Selecting five cards, one at a time without replacement, from a standard deck of cards. The
random variable is the number of red cards obtained.
85)
86) The random variable x represents the number of boys in a family of three children.
Assuming that boys and girls are equally likely, (a) construct a probability distribution,
and (b) graph the distribution.
86)
87) The random variable x represents the number of tests that a patient entering a hospital
will have along with the corresponding probabilities. Graph the probability distribution.
87)
x
0 1 2 3 4
3 5 6 2 1
P(x)
17 17 17 17 17
88) The random variable x represents the number of credit cards that adults have along with
the corresponding probabilities. Graph the probability distribution.
88)
x P(x)
0 0.07
1 0.68
2 0.21
3 0.03
4 0.01
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
89) Find the mean of the binomial distribution for which n = 10 and p = 0.2.
A) 2
B) 10
C) 5
D) 1.26
89)
90) Find the variance of the binomial distribution for which n = 700 and p = 0.88.
A) 8.6
B) 73.92
C) 32.54
D) 616
90)
91) Find the standard deviation of the binomial distribution for which n = 600 and p = 0.86.
A) 8.5
B) 72.24
C) 6.31
D) 516
12
91)
92) A test consists of 770 true or false questions. If the student guesses on each question, what is the
mean number of correct answers?
A) 385
B) 154
C) 0
D) 770
92)
93) A test consists of 70 true or false questions. If the student guesses on each question, what is the
standard deviation of the number of correct answers?
A) 0
B) 2
C) 5.92
D) 4.18
93)
94) In a recent survey, 80% of the community favored building a police substation in their
neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?
A) 10
B) 12
C) 8
D) 15
94)
95) In a recent survey, 80% of the community favored building a police substation in their
neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the
substation?
A) 2.40
B) 1.55
C) 0.98
D) 0.55
95)
96) The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly
selected, what is the mean of the number of houses burglarized?
A) 0.5
B) 1.5
C) 10
D) 1
96)
97) In one city, 33% of adults smoke. In groups of size 90 of adults, what is the variance of the number
that smoke ?
A) 4.46
B) 19.9
C) 9.95
D) 29.7
97)
98) A test consists of 70 multiple choice questions, each with five possible answers, only one of which
is correct. Find the mean and the standard deviation of the number of correct answers.
A) mean: 35; standard deviation: 5.92
B) mean: 14; standard deviation: 3.35
C) mean: 14; standard deviation: 3.74
D) mean: 35; standard deviation: 3.35
98)
99) The probability that an individual is left-handed is 0.1. In a class of 20 students, what is the mean
and standard deviation of the number of left-handers in the class?
A) mean: 20; standard deviation: 1.34
B) mean: 2; standard deviation: 1.41
C) mean: 20; standard deviation: 1.41
D) mean: 2; standard deviation: 1.34
99)
100) A recent survey found that 78% of all adults over 50 wear glasses for driving. In a random sample
of 40 adults over 50, what is the mean and standard deviation of those that wear glasses?
A) mean: 8.8; standard deviation: 5.59
B) mean: 8.8; standard deviation: 2.62
C) mean: 31.2; standard deviation: 5.59
D) mean: 31.2; standard deviation: 2.62
100)
101) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the mean and
standard deviation of the number that never married?
A) mean: 4; standard deviation: 2.4
B) mean: 6; standard deviation: 155
C) mean: 4; standard deviation: 1.55
D) mean: 6; standard deviation: 1.55
101)
13
102) According to police sources, a car with a certain protection system will be recovered 90% of the
time. If 800 stolen cars are randomly selected, what is the mean and standard deviation of the
number of cars recovered after being stolen?
A) mean: 720; standard deviation: 8.49
B) mean: 720; standard deviation: 72
D) mean: 568: standard deviation: 8.49
C) mean: 568: standard deviation: 72
102)
103) The probability that a tennis set will go to a tiebreaker is 15%. In 100 randomly selected tennis
sets, what is the mean and the standard deviation of the number of tiebreakers?
A) mean: 15; standard deviation: 3.57
B) mean: 14; standard deviation: 3.57
C) mean: 15; standard deviation: 3.87
D) mean: 14; standard deviation: 3.87
103)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
104) Assume that male and female births are equally likely and that the birth of any child does
not affect the probability of the gender of any other children. Suppose that 300 couples
each have a baby; find the mean and standard deviation for the number of girls in the 300
babies.
104)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
105) Find the mean of the binomial distribution for which n = 60 and p = 0.2.
A) 60
B) 30
C) 12
D) 3.1
105)
106) Find the variance of the binomial distribution for which n = 800 and p = 0.88.
A) 32.54
B) 704
C) 84.48
D) 9.19
106)
107) Find the standard deviation of the binomial distribution for which n = 400 and p = 0.89.
A) 39.16
B) 6.31
C) 356
D) 6.26
107)
108) A test consists of 850 true or false questions. If the student guesses on each question, what is the
mean number of correct answers?
A) 170
B) 0
C) 850
D) 425
108)
109) A test consists of 910 true or false questions. If the student guesses on each question, what is the
standard deviation of the number of correct answers?
A) 21.33
B) 15.08
C) 2
D) 0
109)
110) In a recent survey, 80% of the community favored building a police substation in their
neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?
A) 12
B) 15
C) 10
D) 8
110)
111) In a recent survey, 80% of the community favored building a police substation in their
neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the
substation?
A) 1.55
B) 0.55
C) 2.40
D) 0.98
111)
112) The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly
selected, what is the mean of the number of houses burglarized?
A) 1.5
B) 10
C) 0.5
D) 1
112)
14
113) In one city, 21% of adults smoke. In groups of size 130 of adults, what is the variance of the
number that smoke ?
A) 27.3
B) 10.78
C) 21.57
D) 4.64
113)
114) A test consists of 30 multiple choice questions, each with five possible answers, only one of which
is correct. Find the mean and the standard deviation of the number of correct answers.
A) mean: 15; standard deviation: 3.87
B) mean: 15; standard deviation: 2.19
C) mean: 6; standard deviation: 2.45
D) mean: 6; standard deviation: 2.19
114)
115) The probability that an individual is left-handed is 0.17. In a class of 40 students, what is the mean
and standard deviation of the number of left-handers in the class?
A) mean: 40; standard deviation: 2.61
B) mean: 40; standard deviation: 2.38
C) mean: 6.8; standard deviation: 2.61
D) mean: 6.8; standard deviation: 2.38
115)
116) A recent survey found that 69% of all adults over 50 wear glasses for driving. In a random sample
of 70 adults over 50, what is the mean and standard deviation of those that wear glasses?
A) mean: 48.3; standard deviation: 3.87
B) mean: 21.7; standard deviation: 6.95
C) mean: 48.3; standard deviation: 6.95
D) mean: 21.7; standard deviation: 3.87
116)
117) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the mean and
standard deviation of the number that never married?
A) mean: 6; standard deviation: 155
B) mean: 4; standard deviation: 2.4
C) mean: 4; standard deviation: 1.55
D) mean: 6; standard deviation: 1.55
117)
118) According to police sources, a car with a certain protection system will be recovered 94% of the
time. If 400 stolen cars are randomly selected, what is the mean and standard deviation of the
number of cars recovered after being stolen?
A) mean: 376; standard deviation: 22.56
B) mean: 376; standard deviation: 4.75
D) mean: 122: standard deviation: 4.75
C) mean: 122: standard deviation: 22.56
118)
119) The probability that a tennis set will go to a tiebreaker is 16%. In 420 randomly selected tennis
sets, what is the mean and the standard deviation of the number of tiebreakers?
A) mean: 67.2; standard deviation: 8.2
B) mean: 67.2; standard deviation: 7.51
C) mean: 63; standard deviation: 8.2
D) mean: 63; standard deviation: 7.51
119)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
120) Assume that male and female births are equally likely and that the birth of any child does
not affect the probability of the gender of any other children. Suppose that 1000 couples
each have a baby; find the mean and standard deviation for the number of girls in the 1000
babies.
15
120)
121) In a pizza takeout restaurant, the following probability distribution was obtained. The
random variable x represents the number of toppings for a large pizza. Graph the
probability distribution.
x
0
1
2
3
4
121)
P(x)
0.30
0.40
0.20
0.06
0.04
122) Use the frequency distribution to (a) construct a probability distribution for the random
variable x represents the number of cars per household in a town of 1000 households, and
(b) graph the distribution.
122)
Cars Households
0
125
1
428
2
256
3
108
4
83
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
123) Assume that male and female births are equally likely and that the birth of any child does not
affect the probability of the gender of any other children. Find the probability of exactly five boys
in ten births.
A) 0.05
B) 0.246
C) 7.875
D) 0.5
123)
124) Assume that male and female births are equally likely and that the birth of any child does not
affect the probability of the gender of any other children. Find the probability of at most three boys
in ten births.
A) 0.300
B) 0.003
C) 0.172
D) 0.333
124)
125) A test consists of 10 true or false questions. To pass the test a student must answer at least eight
questions correctly. If the student guesses on each question, what is the probability that the
student will pass the test?
A) 0.055
B) 0.08
C) 0.8
D) 0.20
125)
126) A test consists of 10 multiple choice questions, each with five possible answers, one of which is
correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses,
what is the probability that the student will pass the test?
A) 0.060
B) 0.377
C) 0.006
D) 0.205
126)
127) In a recent survey, 79% of the community favored building a police substation in their
neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the
building of the police substation.
A) 0.039
B) 0.790
C) 0.571
D) 0.003
127)
16
128) The probability that an individual is left-handed is 0.1. In a class of 44 students, what is the
probability of finding five left-handers?
A) 0.1
B) 0.000
C) 0.178
D) 0.114
128)
129) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample
of 10 adults over 50, what is the probability that at least six wear glasses?
A) 0.850
B) 0.006
C) 0.700
D) 0.200
129)
130) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the probability
that two or fewer were never married?
A) 0.013
B) 0.161
C) 0.167
D) 1.002
130)
131) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the probability
that at least eight were married?
A) 0.013
B) 0.161
C) 0.167
D) 1.002
131)
132) According to police sources, a car with a certain protection system will be recovered 87% of the
time. Find the probability that 4 of 8 stolen cars will be recovered.
A) 0.011
B) 0.87
C) 0.500
D) 0.13
132)
133) The probability that a tennis set will go to a tie-breaker is 17%. What is the probability that two of
three sets will go to tie-breakers?
A) 0.072
B) 0.0289
C) 0.17
D) 0.351
133)
134) Fifty percent of the people that get mail-order catalogs order something. Find the probability that
exactly two of 8 people getting these catalogs will order something.
A) 0.109
B) 0.004
C) 7.000
D) 0.250
134)
135) The probability that a house in an urban area will be burglarized is 3%. If 25 houses are randomly
selected, what is the probability that none of the houses will be burglarized?
A) 0.001
B) 0.000
C) 0.467
D) 0.030
135)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
136) An airline has a policy of booking as many as 150 persons on a plane that seats 140. Past
studies indicate that only 85% of booked passengers show up for their flight. Find the
probability that if the airline books 150 persons for a 140-seat plane, not enough seats will
be available.
136)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
137) Sixty-five percent of men consider themselves knowledgeable football fans. If 12 men are
randomly selected, find the probability that exactly four of them will consider themselves
knowledgeable fans.
A) 0.237
B) 0.020
C) 0.333
D) 0.65
17
137)
138) Assume that male and female births are equally likely and that the birth of any child does not
affect the probability of the gender of any other children. Find the probability of exactly eight boys
in ten births.
A) 0.08
B) 0.044
C) 0.176
D) 0.8
138)
139) Assume that male and female births are equally likely and that the birth of any child does not
affect the probability of the gender of any other children. Find the probability of at most three boys
in ten births.
A) 0.172
B) 0.003
C) 0.333
D) 0.300
139)
140) A test consists of 10 true or false questions. To pass the test a student must answer at least eight
questions correctly. If the student guesses on each question, what is the probability that the
student will pass the test?
A) 0.055
B) 0.8
C) 0.08
D) 0.20
140)
141) A test consists of 10 multiple choice questions, each with five possible answers, one of which is
correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses,
what is the probability that the student will pass the test?
A) 0.205
B) 0.377
C) 0.006
D) 0.060
141)
142) In a recent survey, 73% of the community favored building a police substation in their
neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the
building of the police substation.
A) 0.013
B) 0.094
C) 0.571
D) 0.730
142)
143) The probability that an individual is left-handed is 0.19. In a class of 23 students, what is the
probability of finding five left-handers?
A) 0.217
B) 0.188
C) 0.19
D) 0.000
143)
144) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample
of 10 adults over 50, what is the probability that at least six wear glasses?
A) 0.850
B) 0.006
C) 0.700
D) 0.200
144)
145) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the probability
that two or fewer were never married?
A) 1.002
B) 0.167
C) 0.013
D) 0.161
145)
146) According to government data, the probability that a woman between the ages of 25 and 29 was
never married is 40%. In a random survey of 10 women in this age group, what is the probability
that at least eight were married?
A) 0.013
B) 0.161
C) 1.002
D) 0.167
146)
147) The probability that a tennis set will go to a tie-breaker is 11%. What is the probability that two of
three sets will go to tie-breakers?
A) 0.11
B) 0.261
C) 0.0121
D) 0.032
147)
148) Fifty percent of the people that get mail-order catalogs order something. Find the probability that
exactly five of 8 people getting these catalogs will order something.
A) 0.219
B) 1.750
C) 0.004
D) 0.625
148)
18
149) The probability that a house in an urban area will be burglarized is 4%. If 19 houses are randomly
selected, what is the probability that none of the houses will be burglarized?
A) 0.460
B) 0.000
C) 0.040
D) 0.002
149)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
150) An airline has a policy of booking as many as 150 persons on a plane that seats 140. Past
studies indicate that only 85% of booked passengers show up for their flight. Find the
probability that if the airline books 150 persons for a 140-seat plane, not enough seats will
be available.
150)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
151) Sixty-five percent of men consider themselves knowledgeable football fans. If 10 men are
randomly selected, find the probability that exactly three of them will consider themselves
knowledgeable fans.
A) 0.252
B) 0.65
C) 0.021
D) 0.300
151)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
152) You observe the gender of the next 100 babies born at a local hospital. You count the
number of girls born. Identify the values of n, p, and q, and list the possible values of the
random variable x.
152)
153) Twenty-six percent of people in the United States with Internet access go online to get
news. A random sample of five Americans with Internet access is selected and asked if
they get the news online. Identify the values of n, p, and q, and list the possible values of
the random variable x.
153)
154) Fifty-seven percent of families say that their children have an influence on their vacation
plans. Consider a sample of eight families who are asked if their children influence their
vacation plans. Identify the values of n, p, and q, and list the possible values of the
random variable x.
154)
155) Thirty-eight percent of people in the United States have type O+ blood. You randomly
select 30 Americans and ask them if their blood type is O +. Identify the values of n, p, and
q, and list the possible values of the random variable x.
155)
156) You observe the gender of the next 100 babies born at a local hospital. You count the
number of girls born. Identify the values of n, p, and q, and list the possible values of the
random variable x.
156)
157) Twenty-six percent of people in the United States with Internet access go online to get
news. A random sample of five Americans with Internet access is selected and asked if
they get the news online. Identify the values of n, p, and q, and list the possible values of
the random variable x.
157)
158) Fifty-seven percent of families say that their children have an influence on their vacation
plans. Consider a sample of eight families who are asked if their children influence their
vacation plans. Identify the values of n, p, and q, and list the possible values of the
random variable x.
158)
19
159) Thirty-eight percent of people in the United States have type O+ blood. You randomly
select 30 Americans and ask them if their blood type is O +. Identify the values of n, p, and
q, and list the possible values of the random variable x.
159)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
160) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an
average of three students arrive. Use the Poisson distribution to find the probability that in a
randomly selected office hour in the 10:30 a.m. time slot exactly six students will arrive.
A) 0.0149
B) 0.0025
C) 0.0504
D) 0.0007
160)
161) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an
average of three students arrives. Use the Poisson distribution to find the probability that in a
randomly selected office hour no students will arrive.
A) 0.1108
B) 0.0743
C) 0.0498
D) 0.1225
161)
162) A sales firm receives an average of four calls per hour on its toll-free number. For any given hour,
find the probability that it will receive exactly nine calls. Use the Poisson distribution.
A) 0.0001
B) 0.0132
C) 0.0003
D) 146.3700
162)
163) A sales firm receives an average of three calls per hour on its toll-free number. For any given hour,
find the probability that it will receive at least three calls. Use the Poisson distribution.
A) 0.6138
B) 0.4232
C) 0.5768
D) 0.1891
163)
164) A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100
advertisements, find the probability of receiving at least two orders. Use the Poisson distribution.
A) 0.9596
B) 0.1839
C) 0.9048
D) 0.2642
164)
165) A local fire station receives an average of 0.55 rescue calls per day. Use the Poisson distribution to
find the probability that on a randomly selected day, the fire station will receive fewer than two
calls.
A) 0.087
B) 0.894
C) 0.317
D) 0.106
165)
166) A car towing service company averages two calls per hour. Use the Poisson distribution to
determine the probability that in a randomly selected hour the number of calls is five.
A) 0.0014
B) 0.0018
C) 0.0282
D) 0.0361
166)
167) A book contains 500 pages. If there are 200 typing errors randomly distributed throughout the
book, use the Poisson distribution to determine the probability that a page contains exactly three
errors.
A) 0.1734
B) 0.0129
C) 0.0072
D) 0.0005
167)
168) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an
average of three students arrive. Use the Poisson distribution to find the probability that in a
randomly selected office hour in the 10:30 a.m. time slot exactly four students will arrive.
A) 0.0489
B) 0.1328
C) 0.1680
D) 0.0618
168)
20
169) A statistics professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an
average of three students arrives. Use the Poisson distribution to find the probability that in a
randomly selected office hour no students will arrive.
A) 0.1225
B) 0.1108
C) 0.0498
D) 0.0743
169)
170) A sales firm receives an average of four calls per hour on its toll-free number. For any given hour,
find the probability that it will receive exactly five calls. Use the Poisson distribution.
A) 0.0575
B) 0.1564
C) 0.0954
D) 772.5846
170)
171) A sales firm receives an average of three calls per hour on its toll-free number. For any given hour,
find the probability that it will receive at least three calls. Use the Poisson distribution.
A) 0.1891
B) 0.6138
C) 0.5768
D) 0.4232
171)
172) A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100
advertisements, find the probability of receiving at least two orders. Use the Poisson distribution.
A) 0.9596
B) 0.1839
C) 0.2642
D) 0.9048
172)
173) A local fire station receives an average of 0.55 rescue calls per day. Use the Poisson distribution to
find the probability that on a randomly selected day, the fire station will receive fewer than two
calls.
A) 0.894
B) 0.087
C) 0.317
D) 0.106
173)
174) A car towing service company averages two calls per hour. Use the Poisson distribution to
determine the probability that in a randomly selected hour the number of calls is six.
A) 0.0001
B) 0.0002
C) 0.0120
D) 0.0068
174)
175) A book contains 500 pages. If there are 200 typing errors randomly distributed throughout the
book, use the Poisson distribution to determine the probability that a page contains exactly two
errors.
A) 0.4423
B) 0.0108
C) 0.0893
D) 0.0536
175)
21
Answer Key
Testname: MATH212PROBDISTR
1) A
2) B
3) A
4) A
5) B
6) A
7) A
8) B
9) A
10) A
11) B
12) B
13) B
14) B
15) B
16) B
17) B
18) B
19) A
20) B
21) C
22) D
23) C
24) The student is not correct. For a student to have five accidents is unusual because the probability of this event is 0.026.
25) The sports announcer is correct. For a baseball player to get four or more hits during a World Series is not unusual
because the probability is 0.15625.
26) B
27) A
28) D
29) The student is not correct. For a student to have five accidents is unusual because the probability of this event is 0.026.
30) The sports announcer is correct. For a baseball player to get four or more hits during a World Series is not unusual
because the probability is 0.15625.
31)
x
1 2 3 4 5 6 7
P(x) 0.71 0.12
0
0.12
0
0
0.06
32)
x
0 1 2 3 4 5
P(x) 0.16 0.12 0.48 0.12 0.08 0.04
33)
x
P(x)
0
0.21875
1
0.28125
2
0.21875
3
0.125
4
0.03125
5
0.03125
6
0.0625
7
0.03125
34) B
35) B
22
Answer Key
Testname: MATH212PROBDISTR
36) B
37) (a)
x P(x)
1
0
8
1
3
8
2
3
8
3
1
8
(b)
38)
23
Answer Key
Testname: MATH212PROBDISTR
39)
40)
24
Answer Key
Testname: MATH212PROBDISTR
41) (a)
x
0
1
2
3
4
P(x)
0.125
0.428
0.256
0.108
0.083
(b)
42)
x
1 2 3
P(x) 0.71 0.12
0
4 5
0.12
0
6
0
7
0.06
43)
x
0 1 2 3 4 5
P(x) 0.16 0.12 0.48 0.12 0.08 0.04
44)
x
0
1
2
3
4
5
6
7
45) A
46) D
47) B
48) B
49) B
50) D
51) C
52) D
53) B
P(x)
0.21875
0.28125
0.21875
0.125
0.03125
0.03125
0.0625
0.03125
25
Answer Key
Testname: MATH212PROBDISTR
54) C
55) B
56) D
57) μ = 1.596; σ = 1.098
58) B
59) B
60) C
61) A
62) D
63) C
64) D
65) B
66) A
67) μ = 1.596; σ = 1.098
68) binomial experiment
69) Not a binomial experiment. There are more than two outcomes.
70) Not a binomial experiment. There are more than two outcomes.
71) Not a binomial experiment. There are more than two outcomes.
72) binomial experiment.
73) Not a binomial experiment. There are more than two outcomes.
74) binomial experiment.
75) binomial experiment.
76) Not a binomial experiment. The probability of success is not the same for each trial.
77) binomial experiment
78) Not a binomial experiment. There are more than two outcomes.
79) Not a binomial experiment. There are more than two outcomes.
80) Not a binomial experiment. There are more than two outcomes.
81) binomial experiment.
82) Not a binomial experiment. There are more than two outcomes.
83) binomial experiment.
84) binomial experiment.
85) Not a binomial experiment. The probability of success is not the same for each trial.
26
Answer Key
Testname: MATH212PROBDISTR
86) (a)
x P(x)
1
0
8
1
3
8
2
3
8
3
1
8
(b)
87)
27
Answer Key
Testname: MATH212PROBDISTR
88)
89) A
90) B
91) A
92) A
93) D
94) B
95) B
96) D
97) B
98) B
99) D
100) D
101) C
102) A
103) A
104) μ = np = 300(0.5) = 150; σ = npq = 300(0.5)(0.5) = 8.66
105) C
106) C
107) D
108) D
109) B
110) A
111) A
112) D
113) C
114) D
115) D
116) A
117) C
118) B
119) B
120) μ = np = 1000(0.5) = 500; σ = npq = 1000(0.5)(0.5) = 15.81
28
Answer Key
Testname: MATH212PROBDISTR
121)
122) (a)
x
0
1
2
3
4
P(x)
0.125
0.428
0.256
0.108
0.083
(b)
123)
124)
125)
126)
127)
128)
129)
B
C
A
C
A
C
A
29
Answer Key
Testname: MATH212PROBDISTR
130)
131)
132)
133)
134)
135)
136)
137)
138)
139)
140)
141)
142)
143)
144)
145)
146)
147)
148)
149)
150)
151)
152)
153)
154)
155)
156)
157)
158)
159)
160)
161)
162)
163)
164)
165)
166)
167)
168)
169)
170)
171)
172)
173)
174)
175)
C
C
A
A
A
C
0.0005
B
B
A
A
C
B
B
A
B
D
D
A
A
0.0005
C
n = 100; p = 0.5; q = 0.5; x = 0, 1, 2, . . ., 99, 100
n = 5; p = 0.26; q = 0.84; x = 0, 1, 2, 3, 4, 5
n = 8; p = 0.57; q = 0.43; x = 0, 1, 2, 3, 4, 5, 6, 7, 8
n = 30; p = 0.38; q = 0.62; x = 0, 1, 2, . . ., 29, 30
n = 100; p = 0.5; q = 0.5; x = 0, 1, 2, . . ., 99, 100
n = 5; p = 0.26; q = 0.84; x = 0, 1, 2, 3, 4, 5
n = 8; p = 0.57; q = 0.43; x = 0, 1, 2, 3, 4, 5, 6, 7, 8
n = 30; p = 0.38; q = 0.62; x = 0, 1, 2, . . ., 29, 30
C
C
B
C
D
B
D
C
C
C
B
C
C
A
C
D
30