AnswersAdvanced Algebra Concepts and ConnectionsProperties of Probability Distributions

Properties of Probability Distributions — Quiz Answers

10 verified answers
1
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Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?

A
symmetric
B
constant
C
positively skewed
D
negatively skewed
2
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A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space cap s is equal to GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO If the random variable cap x represents the number of times orange, cap o , is spun, which graph represents the probability distribution?

A
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0, and its height is 0 point 1 2. The second bar is at 1, its height is 0 point 2 5, the 3rd bar is at 2, and its height is 0 point 5; and the 4th bar is at 3, and its height is 0 point 1 2.
B
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 4 0 in increments of 0 point 0 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0; its height is 0 point 1 3. The second bar is at 1; its height is 0, point 3 8. The 3rd bar is at 2, its height is 0 point 3 8, and the 4th bar is at 3, and its height is 0 point 1 2.
C
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 3 point 5 in increments of 0 point 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0, with its height at 1. The second bar is at 1, and its height is 3. The 3rd bar is at 2, and its height is 3; the 4th bar is at 3, and its height is 1.
D
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0 and its height is 0 point 1 2, the second bar is at 1 and its height is 0 point 5, the 3rd bar is at 2 and its height is 0 point 2 5, and the 4th bar is at 3 and its height is 0 point 1 2.
3

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

A
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 7 5' Row 3: Column 1, '1'; Column 2, '0 point 2 5' Row 4: Column 1, '2'; Column 2, '0'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5' Row 3: Column 1, '1'; Column 2, '0 point 3 7 5' Row 4: Column 1, '2'; Column 2, '0 point 1 2 5'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5 6 2 5' Row 3: Column 1, '1'; Column 2, '0 point 3 7 5' Row 4: Column 1, '2'; Column 2, '0 point 0 6 2 5'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5' Row 3: Column 1, '1'; Column 2, '0 point 2 5' Row 4: Column 1, '2'; Column 2, '0 point 2 5'
4

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 cap x represents the distribution of prizes, which graph represents the probability distribution for a randomly selected student?

A
Image with description The bar graph is entitled probability distribution. The horizontal axis lists no prize to 4th prize in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 8 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at No prize and its height is 0 point 68, the second bar is at 1st prize and its height is 0 point 0 1, the 3rd bar is at 2nd prize and its height is 0 point 0 3, the 4th bar is at 3rd prize and its height is 0 point 0 5, and the 5th bar is at 4th prize and its height is 0 point 2.
B
Image with description The bar graph is entitled probability distribution. The horizontal axis lists no prize to 4th prize in increments of 1 and is labeled as x. The vertical axis lists 0 to 40 in increments of 5 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at No prize and its height is 36, the second bar is at 1st prize and its height is 1, the 3rd bar is at 2nd prize and its height is 1, the 4th bar is at 3rd prize and its height is 1, and the 5th bar is at 4th prize and its height is 10.
C
Image with description The bar graph is entitled probability distribution. The horizontal axis lists no prize to 4th prize in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 8 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at No prize and its height is 0 point 7 3, the second bar is at 1st prize and its height is 0 point 0 1, the 3rd bar is at 2nd prize and its height is 0 point 0 1, the 4th bar is at 3rd prize and its height is 0 point 0 1, and the 5th bar is at 4th prize and its height is 0 point 2.
D
Image with description The bar graph is entitled probability distribution. The horizontal axis lists no prize to 4th prize in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 9 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at No prize and its height is 0 point 8, the second bar is at 1st prize and its height is 0 point 0 1, the 3rd bar is at 2nd prize and its height is 0 point 0 3, the 4th bar is at 3rd prize and its height is 0 point 0 5, and the 5th bar is at 4th prize and its height is 0 point 0 8.
5

A family has two children. If cap b represents a boy and cap g represents a girl, the set of outcomes for the possible genders of the children is cap s is equal to BB, BG, GB, GG , with the oldest child listed first in each pair. Let cap x represent the number of times cap g occurs. Which of the following is the probability distribution, cap p sub cap x times x ?

A
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 2 5' Row 3: Column 1, '1'; Column 2, '0 point 7 5' Row 4: Column 1, '2'; Column 2, '0'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 5'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 3 3' Row 3: Column 1, '1'; Column 2, '0 point 3 3' Row 4: Column 1, '2'; Column 2, '0 point 3 3'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 2 5' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 2 5'
6

A teacher assigns a score from 1 to 4 to each student project. The table shows the probability distribution of the scores for a randomly selected student. Which score is most likely? Probability Distribution Score: cap x Probability: cap p times cap x 1 0 point 0 6 2 0 point 2 0 3 0 point 4 8 4 0 point 2 6

A
4
B
2
C
1
D
3
7

Taylor surveys students in one grade level who own at least one pet. She finds that 50 percent 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, cap x , which of the following is the probability distribution, cap p sub x times x ?

A
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 5 3, the second bar is at 2 and its height is 0 point 5, the 3rd bar is at 3 and its height is 0 point 2, and the 4th bar is at 4 and its height is 0 point 2 7.
B
Image with description The bar graph is entitled probability distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 2 8, the second bar is at 2 and its height is 0 point 5, the 3rd bar is at 3 and its height is 0 point 1, and the 4th bar is at 4 and its height is 0 point 1 2.
C
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 7 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 6 1, the second bar is at 2 and its height is 0 point 5, the 3rd bar is at 3 and its height is 0 point 2 2, and the 4th bar is at 4 and its height is 0 point 1 5.
D
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 3, the second bar is at 2 and its height is 0 point 5, the 3rd bar is at 3 and its height is 0 point 1 1, and the 4th bar is at 4 and its height is 0 point 0 8.
8

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 for a randomly selected student. What is the mean of the probability distribution? Probability Distribution Hours Studied: cap x Probability: cap p times cap x 0 point 5 0 point 0 7 1 0 point 2 1 point 5 0 point 4 6 2 0 point 2 2 point 5 0 point 0 7

A
1 point 5 0
B
0 point 8 5
C
0 point 2 0
D
0 point 4 6
9

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 cap s is equal to RR, RB, BR, BB Let cap x represent the number of times blue occurs. Which of the following is the probability distribution, cap p sub cap x times x ?

A
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 3 3' Row 3: Column 1, '1'; Column 2, '0 point 3 3' Row 4: Column 1, '2'; Column 2, '0 point 3 3'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 2 5' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 2 5'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 5'
10

A teacher assigns a score from 1 to 4 to each student project. The table shows the probability distribution of the scores for a randomly selected student. Which score is most likely? Probability Distribution Score: cap x Probability: cap p times cap x 1 0 point 0 6 2 0 point 2 0 3 0 point 4 8 4 0 point 2 6

A
1
B
2
C
3
D
4

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