AnswersGA-Advanced Algebra Concepts and Connections CRRepresenting Data

Properties of Probability Distributions Answers

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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
2
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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
3

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
4

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.
5

A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. If the random variable is “yellow (Y),” which of the following is the correct probability distribution?

A
A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0.5625, 0.375, 0.0625.
Option A
B
A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0.75, 0.25, 0.
Option B
C
A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0.5, 0.375, 0.125.
Option C
D
A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0.5, 0.25, 0.25.
Option D
6

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.
7

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
8

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
9

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
10

A school conducts a recipe contest in which 1 student gets first place, 1 student gets second place, 1 student gets third place, and 10 students tie for fourth place. Fifty students enter the contest. If X represents the distribution of prizes, which graph represents the probability distribution for a randomly selected student?

A
A probability distribution has prizes on the x-axis and probability on the y-axis. The probability of no prize is 0.73; 1st price is 0.01; 2nd price is 0.01; 3rd price is 0.01; 4th price is 0.2.
Option A
B
A probability distribution has prizes on the x-axis and probability on the y-axis. The probability of no prize is 36; 1st price is 1; 2nd price is1; 3rd price is 1; 4th price is 10.
Option B
C
A probability distribution has prizes on the x-axis and probability on the y-axis. The probability of no prize is 0.8; 1st price is 0.01; 2nd price is 0.03; 3rd price is 0.05; 4th price is 0.08.
Option C
D
A probability distribution has prizes on the x-axis and probability on the y-axis. The probability of no prize is 0.68; 1st price is 0.01; 2nd price is 0.03; 3rd price is 0.05; 4th price is 0.2.
Option D

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