AnswersFall 24 GMS Advanced Algebra Concepts and Connections AStandard Deviation

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 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
3

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
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

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
6

Which of the following probability distribution types has a mean, median, and mode that are all equal?

A
constant
B
symmetric
C
positively skewed
D
negatively skewed
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 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
9

A teacher asks her students to write down the number of hours studied, rounded to the nearest half hour. She compiles the results and develops the probability distribution below for a randomly selected student. What is the mean of the probability distribution?Probability DistributionHours Studied: XProbability: P(X)0.50.0710.21.50.4620.22.50.07

A
0.20
B
0.46
C
0.85
D
1.50
10

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.

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