Download Module 5 Test.tst

Module 5 Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
the question.
Calculate the specified probability
1) Suppose that T is a random variable. Given that P(-3.1 ≤ T ≤ 3.1) = 0.25, and that P(K < -3.1) = P(K > 3.1),
find P(K < -3.1).
A) 0.25
B) 1.55
C) 0.375
D) 0.75
Answer: C
Objective: (5.1) Find Probability Using Rules
Determine the possible values of the random variable.
2) The following table displays a frequency distribution for the number of siblings for students in one middle
school. For a randomly selected student in the school, let X denote the number of siblings of the student.
What are the possible values of the random variable X?
Number of siblings
0
1
2 3 4 5 6 7
Frequency 189 245 102 42 24 13 5 2
A) 0, 1, 2, 3, 4, 5, 6, 7
C) 189, 245, 102, 42, 24, 13, 5, 2
B) 7
D) Brother, sister
Answer: A
Objective: (5.1) Find Possible Values of Random Variable
Find the specified probability.
3) A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting
to see the professor is a random variable, X, with the distribution shown in the table.
x
0
1
2
3
4
5
P(X = x) 0.05 0.10 0.40 0.25 0.15 0.05
The professor gives each student 10 minutes. Determine the probability that a student arriving just after
9:00 am will have to wait at least 10 minutes to see the professor.
A) 0.95
B) 0.40
C) 0.20
D) 0.10
Answer: A
Objective: (5.1) Determine Probability of Event
Use random-variable notation to represent the event.
4) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of the two
numbers. Use random-variable notation to represent the event that the absolute value of the difference of
the two numbers is 2.
A) {X = 2}
B) {(1, 3), (2, 4), (3, 5), (4, 6), (3, 1), (4, 2), (5, 3), (6, 4)}
C) X = 2
D) P{X = 2}
Answer: A
Objective: (5.1) Use Random-Variable Notation to Represent Event
1
Provide an appropriate response.
5) True or false? For any discrete random variable, the possible values of the random variable form a finite set
of numbers.
A) True
B) False
Answer: B
Objective: (5.1) *Know Concepts: Discrete Random Variables
Obtain the probability distribution of the random variable.
6) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below:
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the
random variable X. Leave your probabilities in fraction form.
A)
B)
C)
D)
x P(X = x)
x P(X = x)
x P(X = x)
x P(X = x)
0
1/16
0
1/16
0
1/16
1
1/4
1
1/8
1
3/16
1
1/4
2
7/16
2
3/8
2
1/2
2
3/8
3
1/4
3
1/8
3
3/16
3
1/4
4
1/16
4
1/16
4
1/16
4
1/16
Answer: C
Objective: (5.1) Obtain Probability Distribution of Random Variable
Calculate the specified probability
7) Suppose that K is a random variable. Given that P(-2.85 ≤ K ≤ 2.85) = 0.175, and that P(K < -2.85) = P(K >
2.85), find P(K > 2.85).
A) 0.825
B) 0.4125
C) 1.425
D) 0.175
Answer: B
Objective: (5.1) Find Probability Using Rules
8) Suppose that W is a random variable. Given that P(W ≤ 2) = 0.425, find P(W > 2).
A) 2
B) 0.575
C) 0.425
D) 0
Answer: B
Objective: (5.1) Find Probability Using Rules
Use random-variable notation to represent the event.
9) Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Use
random-variable notation to represent the event that the sum of the two numbers is less than 4.
A) {X < 4}
B) (1, 1), (1, 2), (2, 1)
C) {X+Y < 4}
D) {X ≤ 4}
Answer: A
Objective: (5.1) Use Random-Variable Notation to Represent Event
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Determine the possible values of the random variable.
10) Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value of G - R
where G represents the number on the green die and R represents the number on the red die. What are the
possible values of the random variable Y?
A) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
B) 0, 1, 2, 3, 4, 5, 6
C) 0, 1, 2, 3, 4, 5
D) -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6
Answer: A
Objective: (5.1) Find Possible Values of Random Variable
11) For a randomly selected student in a particular high school, let Y denote the number of living
grandparents of the student. What are the possible values of the random variable Y?
A) 0, 1, 2
B) 4
C) 0, 1, 2, 3, 4
D) 1, 2, 3, 4
Answer: C
Objective: (5.1) Find Possible Values of Random Variable
Find the mean of the random variable.
12) The random variable X is the number of golf balls ordered by customers at a pro shop. Its probability
distribution is given in the table.
x
3
6
9 12 15
P(X = x) 0.14 0.13 0.36 0.27 0.10
A) 8.34
B) 9.18
C) 6.51
D) 9
Answer: B
Objective: (5.2) Find Mean of Random Variable Given Probability Distribution
Find the expected value of the random variable.
13) Sue Anne owns a medium-sized business. Use the probability distribution below, where X describes the
number of employees who call in sick on a given day.
Number of Employees Sick
P(X = x)
0
0.1
1
0.35
2
0.3
3
4
0.2 0.05
What is the expected value of the number of employees calling in sick on any given day?
A) 2.00
B) 1.75
C) 1.85
D) 1.00
Answer: B
Objective: (5.2) Find Expected Value of Discrete Random Variable
Find the mean of the random variable.
14) The random variable X is the number of people who have a college degree in a randomly selected group of
four adults from a particular town. Its probability distribution is given in the table.
x P(X = x)
0
0.0256
1
0.1536
2
0.3456
3
0.3456
4
0.1296
A) 2.40
B) 2.00
C) 2.30
D) 2.43
Answer: A
Objective: (5.2) Find Mean of Random Variable Given Probability Distribution
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15) The random variable X is the number that shows up when a loaded die is rolled. Its probability
distribution is given in the table.
x P(X = x)
1
0.14
2
0.11
3
0.15
4
0.10
5
0.14
6
0.36
A) 3.94
B) 4.07
C) 3.50
D) 0.17
Answer: B
Objective: (5.2) Find Mean of Random Variable Given Probability Distribution
The probability distribution of a random variable is given along with its mean and standard deviation. Draw a
probability histogram for the random variable; locate the mean and show one, two, and three standard deviation
intervals.
16) The random variable X is the number of tails when four coins are flipped. Its probability distribution is as
follows.
x
P(X = x)
0
1
16
1
1
4
2
3
8
3
1
4
4
1
16
µ = 2, σ = 1
A)
B)
4
C)
Answer: C
Objective: (5.2) Draw Histogram Showing Mean and Standard Deviation
Find the expected value of the random variable.
17) 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) -$0.40
B) -$1.00
C) -$0.50
D) $0.00
Answer: C
Objective: (5.2) Find Expected Value of Discrete Random Variable
18) The probability distribution below describes the number of thunderstorms that a certain town may
experience during the month of August. Let X represent the number of thunderstorms in August.
Number of storms
P(X = x)
0
0.2
1
0.2
2
0.4
3
0.2
What is the expected value of thunderstorms for the town each August?
A) 2.0
B) 1.6
C) 1.5
D) 1.8
Answer: B
Objective: (5.2) Find Expected Value of Discrete Random Variable
19) A contractor is considering a sale that promises a profit of $34,000 with a probability of 0.7 or a loss (due to
bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected profit?
A) $19,000
B) $18,000
C) $23,800
D) $35,000
Answer: A
Objective: (5.2) Find Expected Value of Discrete Random Variable
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Find the mean of the random variable.
20) The random variable X is the number of houses sold by a realtor in a single month at the Sendsom's Real
Estate office. Its probability distribution is given in the table.
x P(X = x)
0
0.24
1
0.01
2
0.12
3
0.16
4
0.01
5
0.14
6
0.11
7
0.21
A) 3.60
B) 3.40
C) 3.35
D) 3.50
Answer: A
Objective: (5.2) Find Mean of Random Variable Given Probability Distribution
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