Properties of Probability Distributions

Question 1

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?

Revolt · Accepted Answer

positively skewed

Question 2

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?

Revolt · Accepted Answer

3

Question 3

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)?

Revolt · Accepted Answer

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.

Question 4

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?

Revolt · Accepted Answer

4 siblings

Question 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?

Revolt · Accepted Answer

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.

Question 6

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)?

Revolt · Accepted Answer

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.

Question 7

Which of the following describes the probability distribution below?

Revolt · Accepted Answer

The median is greater than the mean, and the majority of the data points are to the right of the mean.

Question 8

Which of the following represents a valid probability distribution?

Revolt · Accepted Answer

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.

Question 9

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)?

Revolt · Accepted Answer

A probability distribution is shown. The probability of 1 is 0.3; 2 is 0.5; 3 is 0.11; 4 is 0.08.

Question 10

Which of the following describes the probability distribution below?

Revolt · Accepted Answer

The mean is greater than the median, and the majority of the data points are to the left of the mean.

Properties of Probability Distributions Answers

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