Calculating and Interpreting z-Scores Answers

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1
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A teacher gave a unit test to both of her statistics classes. The mean test grade for Class A was 77 points, with a standard deviation of 5 points, whereas the mean test grade for Class B was 80, with a standard deviation of 7 points. Kyle, in Class A, received an 82 on the test, and Caleb, in Class B, received an 87. Whose performance on the unit test was better relative to their class?

A
Caleb did better because his z-score is higher than Kyle’s.
B
Kyle did better because his z-score is higher than Caleb’s.
C
Caleb did better because his z-score is closer to the mean.
D
They both performed the same because their z-scores have the same value.
2
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In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5.5 days. One length of gestation had a z-score of –1.70. Which of the following sentences best interprets this z-score?

A
The length of this gestation period was longer than the mean length of gestation periods by 1.7 days.
B
The length of this gestation period was shorter than the mean length of gestation periods by 1.7 days.
C
The length of this gestation period was longer than the mean length of gestation periods by 1.7 standard deviations.
D
The length of this gestation period was shorter than the mean length of gestation periods by 1.7 standard deviations.
3

A popular restaurant advertises that it delivers its orders within 30 minutes. Suppose the average delivery time for one store is 27 minutes with a standard deviation of three minutes. One particular order delivery has a z-score of –2.15. Which of the following statements is not a correct interpretation?

A
The delivery time was 2.15 standard deviations below the average delivery time.
B
The delivery time was less than the average delivery time by 2.15 standard deviations.
C
The delivery time was faster than the average delivery time by 2.15 standard deviations.
D
The delivery time was slower than the average delivery time by 2.15 standard deviations.
4

On a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2. What is the test grade, rounded to the nearest whole number, with a z-score of 2.4?

A
65
B
83
C
90
D
95
6

Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother’s score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire’s mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance?

A
Claire did better because her z-score is greater than her mother’s.
B
Claire’s mother did better because her z-score is greater than Claire’s.
C
Claire did better because her z-score is closer to the mean than her mother’s.
D
Claire’s mother did better because her z-score is closer to the mean than Claire’s.
8

In a statistics class, students were asked how many siblings they have. Their responses are shown.2, 3, 1, 3, 5, 3, 3, 3, 6, 3, 5, 0, 3

A
–0.67
B
–0.13
C
0.13
D
0.67
9

On a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2. One test grade has a z-score of 2.4. Which of the following statements gives the best interpretation of this z-score?

A
This student’s test grade was higher than 2.4% of the other students’ test grades.
B
This student’s test grade was 2.4 standard deviations above the mean test grade.
C
This student’s test grade was 2.4 standard deviations below the mean test grade.
D
The student’s test grade was lower than 2.4% of the other students’ test grades.
10

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5.5 days. What is the z-score for a gestation period that lasts 290 days?

A
–1.09
B
–1.00
C
1.00
D
1.09

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