Q R2.1. Is Paul tall? According to the N... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

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 $85 t h$ 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

Part (a) Step 1: Given information

x = 179 c m 渭 = 170 c m 蟽 = 7.5 c m

Part (a) Step 2: Concept

The Formula used: $z = \frac{x 鈭� 渭}{蟽}$

Part (a) Step 3: Calculation

$z = \frac{x 鈭� 渭}{蟽} z = 179 鈭� 170 / 7.5 z = 1.20$

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

Part (b) Step 1: Explanation

The $85 t h$ 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.