PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Question
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Chapter 2.1, Problem 3E

(a)

To determine

Antawn’s percentile having head circumference of 22.4 inches.

(a)

Expert Solution
Check Mark

Answer to Problem 3E

Percentile that corresponds with head circumference of 22.4 inches is 33rd percentile.

Explanation of Solution

Given information:

Measurements of head circumference (in inches):

  PRACTICE OF STATISTICS F/AP EXAM, Chapter 2.1, Problem 3E , additional homework tip  1

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Now,

Sort all the data values in ascending order:

20.8, 20.8, 21.0, 21.5, 21.6, 21.7, 21.9, 22.0, 22.2, 22.3, 22.4, 22.5, 22.5, 22.6, 22.6, 22.7, 22.7, 22.7, 23.0, 23.0, 23.1, 23.3, 23.4, 23.5, 23.5, 23.9, 23.9, 24.0, 24.2, 25.6.

Note that

10 of the 30 data values are smaller than 22.4.

Percentile can be determined as the number of data values that are less than the individual’s data value ( n ), divided by the total number of data values ( N ), written as percentage.

  Percentile=nN×100%=1030×100%=0.33×100%=33%

Thus,

Percentile that corresponds with head circumference of 22.4 inches is 33rd percentile.

(b)

To determine

Head circumference of the player at the 90th percentile of the distribution.

(b)

Expert Solution
Check Mark

Answer to Problem 3E

Head circumference at the 90thpercentile is 24.0 inches.

Explanation of Solution

Given information:

Measurements of head circumference (in inches):

  PRACTICE OF STATISTICS F/AP EXAM, Chapter 2.1, Problem 3E , additional homework tip  2

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Now,

Sort all the data values in ascending order:

20.8, 20.8, 21.0, 21.5, 21.6, 21.7, 21.9, 22.0, 22.2, 22.3, 22.4, 22.5, 22.5, 22.6, 22.6, 22.7, 22.7, 22.7, 23.0, 23.0, 23.1, 23.3, 23.4, 23.5, 23.5, 23.9, 23.9, 24.0, 24.2, 25.6.

Note that

The data set consists of 30 data values.

Such that

  N=30

The data value represented by the xth percentile has x% of the data values below it.

Then

90th percentile has 90% of the 30 data values below it.

Calculate 90% of 30 data values:

  n=90%×N=90100×30=910×30=27

We have

27 out of 30 data values are smaller than 90th percentile.

90th percentile needs to be the 28th data value in the ascending order, and that is 24.0.

Thus,

Head circumference of the player at the 90thpercentile of the distribution is 24.0 inches.

Chapter 2 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.2 - Prob. 65ECh. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Prob. 75ECh. 2.2 - Prob. 76ECh. 2.2 - Prob. 77ECh. 2.2 - Prob. 78ECh. 2.2 - Prob. 79ECh. 2.2 - Prob. 80ECh. 2.2 - Prob. 81ECh. 2.2 - Prob. 82ECh. 2.2 - Prob. 83ECh. 2.2 - Prob. 84ECh. 2.2 - Prob. 85ECh. 2.2 - Prob. 86ECh. 2.2 - Prob. 87ECh. 2.2 - Prob. 88ECh. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Prob. 91ECh. 2.2 - Prob. 92ECh. 2 - Prob. R2.1RECh. 2 - Prob. R2.2RECh. 2 - Prob. R2.3RECh. 2 - Prob. R2.4RECh. 2 - Prob. R2.5RECh. 2 - Prob. R2.6RECh. 2 - Prob. R2.7RECh. 2 - Prob. R2.8RECh. 2 - Prob. R2.9RECh. 2 - Prob. T2.1SPTCh. 2 - Prob. T2.2SPTCh. 2 - Prob. T2.3SPTCh. 2 - Prob. T2.4SPTCh. 2 - Prob. T2.5SPTCh. 2 - Prob. T2.6SPTCh. 2 - Prob. T2.7SPTCh. 2 - Prob. T2.8SPTCh. 2 - Prob. T2.9SPTCh. 2 - Prob. T2.10SPTCh. 2 - Prob. T2.11SPTCh. 2 - Prob. T2.12SPTCh. 2 - Prob. T2.13SPT
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