AnswersNC-Math 4Discrete Random Variables – Mean

Discrete Random Variables – Mean Answers

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A professional basketball player typically attempts 8 free throws per game. Let X represent the number of free throws made out of 8. The distribution for X is shown in the table.What is the standard deviation of the distribution?

Question illustration
A
1.18
B
1.40
C
1.96
D
2.58
2
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Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.

Question illustration
A
The center for the distribution of scores appears to be lower for subject B than for subject A.
B
The center for the distribution of subject A is approximately 3, while the center for subject B is approximately 4.
C
The center for the distribution of scores appears to be higher for subject B than for subject A.
D
The center for the distribution of scores appears to be about the same for both subjects.
3

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
0.89
B
0.95
C
1.41
D
1.99
4

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject’s standardized test is given in the table.

Question illustration
A
2.5
B
2.95
C
3
D
3.5
5

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.What is the median of the distribution?

Question illustration
A
3
B
3.5
C
4
D
4.2
6

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.Which is the correct interpretation of the standard deviation?

Question illustration
A
The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.96 eggs.
B
The mean number of eggs laid on a randomly selected day would typically vary by 1.96 from the expected number of eggs.
C
The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.4 eggs.
D
The mean number of eggs laid on a randomly selected day would typically vary by 1.4 from the expected number of eggs.
7

Hannah and Claire each have a chicken coop with 6 hens. Let H represent the total number of eggs the hens lay on a randomly chosen day in Hannah’s coop and let C represent the total number of eggs the hens lay on a randomly chosen day in Claire’s coop. The two distributions are displayed in the table and histograms.

Question illustration
A
Hannah’s hens appear to lay more eggs, on average, than Claire’s hens.
B
Hannah’s hens are expected to lay 4 eggs in a day. Claire’s hens are expected to lay 3 eggs in a day.
C
Hannah’s hens appear to lay fewer eggs, on average, than Claire’s hens.
D
Claire’s hens appear to lay about the same number of eggs, on average, as Hannah’s hens.
8

The owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table.

Question illustration
A
2
B
2.1
C
2.5
D
3
9

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.

Question illustration
A
2
B
3
C
2.98
D
3.50
10

Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.What is the mean of the distribution?

Question illustration
A
3
B
3.5
C
4
D
4.2

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