AnswersConcepts in Probability and Statistics AProperties of Probability Distributions

Properties of Probability Distributions Answers

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A spinner is divided into two equal parts, one red and one blue. The set of possible outcomes when the spinner is spun twice is S = {RR, RB, BR, BB}. Let X represent the number of times blue occurs. Which of the following is the probability distribution, PX(x)?

A
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.25, 0.5, 0.25.
Option A
B
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.33, 0.33, 0.33.
Option B
C
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.5, 0.5, 0.
Option C
D
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0, 0.5, 0.5.
Option D
2
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The number of siblings each student at a softball game has is recorded. The graph below shows the probability distribution of having any number of siblings, X, for a randomly selected student. Which number of siblings is least likely?

Question illustration
A
0 siblings
B
3 siblings
C
4 siblings
D
5 siblings
3

Which of the following describes the probability distribution below?

Question illustration
A
The mean is greater than the median, and the majority of the data points are to the left of the mean.
B
The mean is greater than the median, and the majority of the data points are to the right of the mean.
C
The median is greater than the mean, and the majority of the data points are to the left of the mean.
D
The median is greater than the mean, and the majority of the data points are to the right of the mean.
4

Which of the following represents a valid probability distribution?

A
A 2-column table labeled Probability Distribution A has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries negative 0.14, 0.6, 0.25, 0.29.
Option A
B
A 2-column table labeled Probability Distribution B has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0, 0.45, 0.16, 0.39.
Option B
C
A 2-column table labeled Probability Distribution C has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0.45, 1.23, negative 0.87, 0.19.
Option C
D
A 2-column table labeled Probability Distribution D has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled P (x) with entries 0.87, 0.56, 0, 1.38.
Option D
5

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.
6

A teacher assigns a score from 1 to 4 to each student project. The table below shows the probability distribution of the scores for a randomly selected student. Which score is most likely?Probability DistributionScore: XProbability: P(X)10.0620.2030.4840.26

A
1
B
2
C
3
D
4
7

Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. Eight of the students in the grade own 1 pet. Considering the number of pets as the random variable, X, which of the following is the probability distribution, PX(x)?

A
A probability distribution is shown. The probability of 1 is 0.3; 2 is 0.5; 3 is 0.11; 4 is 0.08.
Option A
B
A probability distribution is shown. The probability of 1 is 0.28; 2 is 0.5; 3 is 0.1; 4 is 0.13.
Option B
C
A probability distribution is shown. The probability of 1 is 0.61; 2 is 0.5; 3 is 0.22; 4 is 0.15.
Option C
D
A probability distribution is shown. The probability of 1 is 0.53; 2 is 0.5; 3 is 0.2; 4 is 0.27.
Option D
8

A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX(x)?

A
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.25, 0.5, 0.25.
Option A
B
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.33, 0.33, 0.33.
Option B
C
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0.25, 0.75, 0.
Option C
D
A 2-column table has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0, 0.5, 0.5.
Option D
9

The graph below shows the experimental probability of a runner finishing in first place (1), in second place (2), in third place (3), or not placing (4). Which of the following describes the probability distribution?

Question illustration
A
constant
B
symmetric
C
negatively skewed
D
positively skewed
10

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

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