Normal Distributions

Question 1

At age six, Kylie is 50 inches tall. Her height has a z-score of 1.8. At age four, Hannah is 48 inches tall. Her height has a z-score of 2.1. Relative to girls their ages, who is taller?

Revolt · Accepted Answer

Hannah is taller because her z-score is higher than Kylie’s z-score.

Question 2

A runner’s distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner’s times has a z-score of –1.76. What is the runner’s time?

Revolt · Accepted Answer

3.18 minutes

Question 3

A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the number of points the athlete scored was 1.2 standard deviations below the mean. Which of the following is the z-score for the number of points scored?

Revolt · Accepted Answer

–1.2

Question 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?

Revolt · Accepted Answer

90

Question 5

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?

Revolt · Accepted Answer

They both performed the same because their z-scores have the same value.

Question 6

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

Revolt · Accepted Answer

–0.67

Question 7

Currently, professional men’s basketball players score an average of 18.2 points per game with a standard deviation of 4.5 points. The current top-scoring professional basketball player scores an average of 36.2 points per game. In one season in the 1990s, professional basketball players averaged 13.2 points per game with a standard deviation of 3.7 points. The top-scoring professional basketball player averaged 30.1 points per game. Which player did better relative to his peers?

Revolt · Accepted Answer

The 1990s basketball player did better than the current basketball player because his z-score is higher.

Question 8

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?

Revolt · Accepted Answer

This student’s test grade was 2.4 standard deviations above the mean test grade.

Question 9

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?

Revolt · Accepted Answer

Claire’s mother did better because her z-score is greater than Claire’s.

Question 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?

Revolt · Accepted Answer

1.09

Normal Distributions Answers

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