AnswersConcepts in Probability and Statistics - MA3120 ICUnit Test

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A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift?Probability DistributionHours Worked: XProbability: P(X)30.14?50.1460.370.3680.06

A
0
B
1
C
2
D
4
2
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The circle below has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters.What is the probability that a point chosen at random is in the blue region?

Question illustration
A
StartFraction 2 over 157 EndFraction
Option A
B
StartFraction 2 over 155 EndFraction
Option B
C
StartFraction 155 over 159 EndFraction
Option C
D
StartFraction 155 over 157 EndFraction
Option D
3

A six-sided number cube is rolled twice. Which expression can be used to find P(5, then3)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

best

t
two or more events that have the same probabilities.
t
two or more events that do not have the same probabilities.
a
a group of events whose later outcomes are not affected by previous outcomes.
a
a group of events whose later outcomes are affected by previous outcomes.
5

The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distribution below. What is the probability that a worker chosen at random works at least 8 hours?

Question illustration
A
0.62
B
0.78
C
0.84
D
0.96
6

Which formula finds the probability that a point on the grid below will be in the blue area?

Question illustration
A
P (blue) = StartFraction total number of squares over number of blue squares EndFraction
Option A
B
P (blue) = StartFraction number of blue squares over total number of squares EndFraction
Option B
C
P (blue) = StartFraction number of blue squares over number of white squares EndFraction
Option C
D
P (blue) = StartFraction number of white squares over number of blue squared EndFraction
Option D
7

Which of the following is a valid probability distribution?

A
Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2.
Option A
B
Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1.
Option B
C
Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1.
Option C
D
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Option D
8

A point is randomly chosen on the grid shown below.What is the likelihood that the point is in the blue section of the grid?

Question illustration
A
It is certain.
B
It is impossible.
C
It is likely.
D
It is unlikely.
9

A coin is thrown at random into the rectangle below.What is the likelihood that the coin will land in the green region?

Question illustration
A
It is certain.
B
It is impossible.
C
It is likely.
D
It is unlikely.
10

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house?Age of HouseNumber of Houses115220325430

A
A probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.
Option A
B
A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.
Option B
C
A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.
Option C
D
A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.
Option D
11

Luka has a bag containing 5 socks: 3 red, 1 white, and 1 black. He draws 1 sock out of the bag, replaces it, and then draws another sock.What is the probability that he will draw a black sock and then a red sock, P(black, then red)?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Aaron, Bob, and Charlotte are running a race. Which event would be considered dependent?

d
determining the chance that Bob comes in first or third
d
determining whose coach runs the stopwatch
d
determining which person begins on the inside lane
d
determining first, second, and third place runners
13

A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability distribution below?

Question illustration
A
0.2
B
0.4
C
1
D
3
14

A coin is flipped, then a number cube is rolled. The tree diagram shows the possible outcomes.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

Which of the following describes the probability distribution below?

Question illustration
A
The median is greater than the mean, and the majority of the data points are to the left of the mean.
B
The median is greater than the mean, and the majority of the data points are to the right of the mean.
C
The mean is greater than the median, and the majority of the data points are to the left of the mean.
D
The mean is greater than the median, and the majority of the data points are to the right of the mean.
16

A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of 50 spins. She computes and graphs the relative frequencies for each number. Which of the following describes the probability distribution?

Question illustration
A
constant
B
symmetric
C
negatively skewed
D
positively skewed
17

Spinning a 4-section spinner twice can be described as which type of event?

A
It is an independent event. The outcome of the second spin is unaffected by the outcome of the first spin.
B
It is a dependent event. The outcome of the second spin is affected by the outcome of the first spin.
C
It is a simple event. Spinning a spinner is a single event.
D
It is an impossible event. A spinner cannot land in two sections.
18

Khalil has a game board as shown below, which is a square with 20-cm sides. The area of the largest circle is 314 square centimeters.What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?

Question illustration
A
50%
B
62.5%
C
75%
D
78.5%
19

Simon designed the game below, which is played by throwing one dart onto the board.Which probability would be least likely when throwing one dart, assuming that the dart will land on the board?

Question illustration
A
scoring exactly 20
B
scoring 15 or greater
C
scoring 10 or greater
D
scoring 5 or greater
20

best

Question illustration
T
They are independent because P(X) · P(Y) = P(X and Y).
T
They are independent because P(X) + P(Y) = P(X and Y).
T
They are dependent because P(X) · P(Y) = P(X and Y).
T
They are dependent because P(X) + P(Y) = P(X and Y).

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