AnswersVA StatisticsCalculating and Interpreting z-Scores

Calculating and Interpreting z-Scores — Quiz Answers

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1
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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 negative 2 point 1 5 Which of the following statements is not a correct interpretation?

A
The delivery time was faster than the average delivery time by 2 point 1 5 standard deviations.
B
The delivery time was 2 point 1 5 standard deviations below the average delivery time.
C
The delivery time was less than the average delivery time by 2 point 1 5 standard deviations.
D
The delivery time was slower than the average delivery time by 2 point 1 5 standard deviations.
6

On a unit test in a statistics class, the teacher determines that the mean test grade was 77 point 5 with a standard deviation of 5 point 2 One test grade has a z -score of 2 point 4 Which of the following statements gives the best interpretation of this z -score?

A
This student’s test grade was higher than 2 point 4 percent of the other students’ test grades.
B
This student’s test grade was 2 point 4 standard deviations below the mean test grade.
C
This student’s test grade was 2 point 4 standard deviations above the mean test grade.
D
The student’s test grade was lower than 2 point 4 percent of the other students’ test grades.
7

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5 point 5 days. One length of gestation had a z -score of negative 1 point 7 0 Which of the following sentences best interprets this z -score?

A
The length of this gestation period was shorter than the mean length of gestation periods by 1 point 7 days.
B
The length of this gestation period was longer than the mean length of gestation periods by 1 point 7 standard deviations.
C
The length of this gestation period was longer than the mean length of gestation periods by 1 point 7 days.
D
The length of this gestation period was shorter than the mean length of gestation periods by 1 point 7 standard deviations.
9

Currently, professional men’s basketball players score an average of 18 point 2 points per game with a standard deviation of 4 point 5 points. The current top-scoring professional basketball player scores an average of 36 point 2 points per game. In one season in the 1990s, professional basketball players averaged 13 point 2 points per game with a standard deviation of 3 point 7 points. The top-scoring professional basketball player averaged 30 point 1 points per game. Which player did better relative to his peers?

A
The current basketball player did better than the 1990s basketball player because his z -score is higher.
B
The 1990s basketball player did better than the current basketball player because his z -score is closer to the mean.
C
The current basketball player did better than the 1990s basketball player because his z -score is closer to the mean.
D
The 1990s basketball player did better than the current basketball player because his z -score is higher.
10

At age six, Kylie is 50 inches tall. Her height has a z -score of 1 point 8 At age four, Hannah is 48 inches tall. Her height has a z -score of 2 point 1 Who is taller?

A
Kylie is taller because her z -score is lower than Hannah’s z -score.
B
Hannah is taller because her z -score is closer to the mean than Kylie’s z -score.
C
Kylie is taller because her z -score is closer to the mean than Hannah’s z -score.
D
Hannah is taller because her z -score is higher than Kylie’s z -score.

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