Q.6.63 The heights of the 430聽National... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 6: Q.6.63 (page 389)

The heights of the $430$ National Basketball Association players were listed on team rosters at the start of the $2005 鈥� 2006$ season. The heights of basketball players have an approximately normal distribution with mean, $碌 = 79$ inches and a standard deviation, $蟽 = 3.89$ inches. For each of the following heights, calculate the z-score and interpret it using complete sentences
a. $77$ inches
b. $85$ inches
c. If an NBA player reported his height had a z-score of $3.5$ , would you believe him? Explain your answer

Short Answer

Expert verified

The z-score $77$ inch height is $- 0.5141$ that is negative So, the $77$ inch is shorter that the average height of players.
The z-score of $85$ is $1.5424$ that is positive. So the height $85$ is taller than the height of the all players.
The obtained height is $92.615$ inches and it is more than the mean height of $79$ inches. So the claim of the players can not believe.

Step by step solution

Given information (Part a)

Given in the question that

Mean $= 79$

Standard deviation $= 3.89$

$X ~ N (79, 3.89)$

Solution (Part a)

We need to calculate the z-score of $x = 77$

$z = \frac{x 鈭� 渭}{蟽}$

$= \frac{77 鈭� 79}{3.89}$

$= 鈭� 0.5141$

Given information (Part b)

Given in the question that

Mean $= 79$

Standard deviation $= 3.89$

$X ~ N (79, 3.89)$

Solution (part b)

Here we need to find the z-score of $x = 85$

$z = \frac{x 鈭� 渭}{蟽}$

$= \frac{85 鈭� 79}{3.89}$

$= 1.5424$

Given information (Part c)

Given in the question that

Mean $= 79$

Standard deviation $= 3.89$

$X ~ N (79, 3.89)$

Solution (Part c)

Here the z-score is given as $3.5$ .So, we need to find the height of the players.

$z = \frac{x 鈭� 渭}{蟽}$

$3.5 = \frac{x 鈭� 79}{3.89}$

$x = 3.5 脳 3.89 + 79$

$= 92.615$

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91影视

Short Answer

Step by step solution

Given information (Part a)

Solution (Part a)

Given information (Part b)

Solution (part b)

Given information (Part c)

Solution (Part c)

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