AnswersNC-Math 4Introduction to Random Variables

Introduction to Random Variables Answers

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1
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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
The probability of a randomly selected test having a score of at most 4 is 0.36.
B
The probability of a randomly selected test having a score of at least 4 is 0.36.
C
The probability of a randomly selected test having a score lower than 4 is 0.85.
D
The probability of a randomly selected test having a score higher than 4 is 0.15.
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 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
0.20
B
0.26
C
0.38
D
0.64
3

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student.

Question illustration
A
0.17
B
0.31
C
0.43
D
0.74
4

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is displayed in the histogram.

Question illustration
A
skewed left
B
skewed right
C
uniform, symmetric
D
approximately Normal
5

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table.Which of the following histograms correctly displays the distribution?

Question illustration
A
A histogram titled free throws has x = number of successful free throws on the x-axis, and probability on the y-axis. 0, 0.002; 1, 0.009; 2, 0.22; 3, 0.28; 4, 0.23; 5, 0.12; 6, 0.04; 7, 0.008; 8, 0.002.
Option A
B
A histogram titled free throws has x = number of successful free throws on the x-axis, and probability on the y-axis. 0, 0.002; 1, 0.008; 2, 0.04; 3, 0.12; 4, 0.23; 5, 0.28; 6, 0.21; 7, 0.09; 8, 0.02.
Option B
C
A histogram titled free throws has x = number of successful free throws on the x-axis, and probability on the y-axis. 0, 0.26; 1, 0.14; 2, 0.06; 3, 0.03; 4, 0.02; 5, 0.03; 6, 0.06; 7, 0.14; 8, 0.26.
Option C
D
A histogram titled free throws has x = number of successful free throws on the x-axis, and probability on the y-axis. 0, 002; 1, 0.03; 2, 0.11; 3, 0.22; 4, 0.27; 5, 0.22; 6, 0.11; 7, 0.03; 8, 0.002.
Option D
6

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities 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
0.28
B
0.55
C
0.72
D
0.83
7

The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities 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
P(X ≤ 3)
B
P(X < 3)
C
P(X ≥ 3)
D
P(X > 3)
8

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table.

Question illustration
A
0.2
B
0.4
C
0.6
D
0.8
9

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
0.26
B
0.36
C
0.62
D
0.66
10

The grade distribution for students in the introductory statistics class at a local community college are displayed in the table. In this table, A = 4, B = 3, etc. Let X represent the grade for a randomly selected student.

Question illustration
A
0.17
B
0.26
C
0.48
D
0.91

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