Answers NY-Algebra II Term 2 HillcrestProperties of Probability Distributions

Properties of Probability Distributions Answers

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

A probability distribution is shown. The probability of 1 is 0.28; 2 is 0.5; 3 is 0.1; 4 is 0.13.

A probability distribution is shown. The probability of 1 is 0.61; 2 is 0.5; 3 is 0.22; 4 is 0.15.

A probability distribution is shown. The probability of 1 is 0.53; 2 is 0.5; 3 is 0.2; 4 is 0.27.

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Which of the following describes the probability distribution below?

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

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

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

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

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?

constant

symmetric

negatively skewed

positively skewed

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

0.20

0.46

0.85

1.50

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?

0.2

0.4

Which of the following describes the probability distribution below?

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

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

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

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

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 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 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.

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.

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.

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.

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 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.

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.

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.

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.

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

constant

symmetric

positively skewed

negatively skewed

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Properties of Probability Distributions Answers

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