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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor
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Is Paul tall? According to the National Center for Health Statistics, the distribution

Chapter 2, Problem R2.1

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QUESTION:

Is Paul tall? According to the National Center for Health Statistics, the distribution of heights for 15-year-old males has a mean of 170 centimeters (cm) and a standard deviation of 7.5 cm. Paul is 15 years old and 179 cm tall. (a) Find the z-score corresponding to Pauls height. Explain what this value means. (b) Pauls height puts him at the 85th percentile among 15-year-old males. Explain what this means to someone who knows no statistics.

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QUESTION:

Is Paul tall? According to the National Center for Health Statistics, the distribution of heights for 15-year-old males has a mean of 170 centimeters (cm) and a standard deviation of 7.5 cm. Paul is 15 years old and 179 cm tall. (a) Find the z-score corresponding to Pauls height. Explain what this value means. (b) Pauls height puts him at the 85th percentile among 15-year-old males. Explain what this means to someone who knows no statistics.

ANSWER:

Step 1 of 2

Given that the distribution of heights for 15-year-old males has a mean of 170 centimeters (cm) and a standard deviation of 7.5 cm. Also, given that Paul is 15 years old and 179 cm tall.

(a) Find the z-score corresponding to Pauls height. Explain what this value means.

The z-score is calculated using the formula:

Where,

is the mean.

is standard deviation.

The z-score corresponding to Pauls height is given as:

Therefore, the z-score corresponding to Paul’s height is .

This means that Paul is taller than the average of his age and 1.20 standard deviation above the average male height of his age.

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