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In a survey of men in the United States (ages 20 to 29), the mean. height was 69.9 inches with a standard deviation of 3.0 inches. Assume the height data is normally distributed. Zak's height has a z-score of-1.7. Which one of the following statements is true? O Zak's height is in the lower 2.5% of men's heights (ages 20 to 29). O Zak is 68.2 inches tall O Zak is shorter than 64.8 inches. O Zak is taller than 72.9 inches.

In a survey of men in the United States (ages 20 to 29), the mean. height was 69.9 inches with a standard deviation of 3.0 inches. Assume the height data is normally distributed. Zak's height has a z-score of-1.7. Which one of the following statements is true? O Zak's height is in the lower 2.5% of men's heights (ages 20 to 29). O Zak is 68.2 inches tall O Zak is shorter than 64.8 inches. O Zak is taller than 72.9 inches.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Understanding Z-Scores and Normal Distribution in Height Data** In a survey of men in the United States (ages 20 to 29), the mean height was recorded as 69.9 inches with a standard deviation of 3.0 inches. Assuming the height data is normally distributed, Zak's height has a z-score of -1.7. Which one of the following statements is true? - O Zak's height is in the lower 2.5% of men's heights (ages 20 to 29). - O Zak is 68.2 inches tall. - O Zak is shorter than 64.8 inches. - O Zak is taller than 72.9 inches. **Explanation:** The z-score of a data point tells us how many standard deviations away it is from the mean. A z-score of -1.7 indicates that Zak's height is 1.7 standard deviations below the mean. In a normal distribution, approximately 95% of data falls within 2 standard deviations of the mean. Therefore, a z-score of -1.7 is within the lowest 2.5% of the distribution, corresponding to the first statement being true. Understanding z-scores helps interpret how Zak's height compares to the general population of men in this age group.
Transcribed Image Text:**Title: Understanding Z-Scores and Normal Distribution in Height Data** In a survey of men in the United States (ages 20 to 29), the mean height was recorded as 69.9 inches with a standard deviation of 3.0 inches. Assuming the height data is normally distributed, Zak's height has a z-score of -1.7. Which one of the following statements is true? - O Zak's height is in the lower 2.5% of men's heights (ages 20 to 29). - O Zak is 68.2 inches tall. - O Zak is shorter than 64.8 inches. - O Zak is taller than 72.9 inches. **Explanation:** The z-score of a data point tells us how many standard deviations away it is from the mean. A z-score of -1.7 indicates that Zak's height is 1.7 standard deviations below the mean. In a normal distribution, approximately 95% of data falls within 2 standard deviations of the mean. Therefore, a z-score of -1.7 is within the lowest 2.5% of the distribution, corresponding to the first statement being true. Understanding z-scores helps interpret how Zak's height compares to the general population of men in this age group.
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