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Chapter 2: Q R2.1. (page 144)

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 Paul鈥檚 height. Explain what this value means.

b. Paul鈥檚 height puts him at the 85th percentile among 15-year-old males. Explain what this means to someone who knows no statistics.

Short Answer

Expert verified

Part (a) z=1.20

Part (b) The researcher is taller than 85% of the population of 15-year-old boys or shorter than 15% of the population of 15-year-old males.

Step by step solution

01

Part (a) Step 1: Given information

x=179cm渭=170cm蟽=7.5cm
02

Part (a) Step 2: Concept

The Formula used: z=x鈭�渭蟽

03

Part (a) Step 3: Calculation

z=x鈭�渭蟽z=179鈭�170/7.5z=1.20

It means that the researcher's average height is 170cm, with a standard deviation of 1.20The researcher's height would be between 168.8and 171.2cm.

04

Part (b) Step 1: Explanation

The 85th percentile is a data point in which 85 percent of the data is less than or equal to it. It also signifies that 15% of the data is larger than or equal to the data point, implying that the researcher is taller than 85% of the population of 15-year-old boys or shorter than 15% of the population of 15-year-old males.

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