Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 17, Problem 67E

Percentiles. The pth percentile of a sorted data set is a number x p such that p% of the data fall at or below x p and ( 100 p ) of the data fall at or above x p . (For details, see Chapter 15, Section 15.2.) For normally distributed data sets, there are detailed statistical tables that give the location of the pth percentile for every possible p between 1 and 99. The following table is an abbreviated version giving the approximate location of some of the more frequently used percentiles in a normal distribution with mean μ and standard deviation σ . For approximately normal distributions, Table 17-19 can be used to estimate these percentiles.

Table 17-9

Percentile Approximate location Percentile Approximate location
99th μ + 2.33 σ 1st μ 2.33 σ
95th μ + 1.65 σ 5th μ 1.65 σ
90th μ + 1.28 σ 10th μ 1.28 σ
80th μ + 0.84 σ 20th μ 0.84 σ
75th μ + 0.675 σ 25th μ 0.675 σ
70th μ + 0.52 σ 30th μ 0.52 σ
60th μ + 0.25 σ 40th μ 0.25 σ
50th μ

In Exercises 67 through 73, you should use the table to make your estimates.

The distribution of weights for six-month baby boys has mean μ = 8.16 kg and standard deviation σ = 0.95 kg. (see Exercise 53).

a. Suppose that a six-month-old boy weighs in the 95th percentile of his age group. Estimate his weight in kilograms rounded to two decimal places.

b. Suppose that a six-month-old baby boy weighs in the 20th percentile of his age group. Estimate his weight in kilograms rounded to two decimal places.

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Chapter 17 Solutions

Excursions in Modern Mathematics (9th Edition)

Ch. 17 - Explain why a distribution with median M=82, mean...Ch. 17 - Explain why a distribution with median M=453, mean...Ch. 17 - Explain why a distribution with =195, Q1=180 and...Ch. 17 - Explain why a distribution with M==47, Q1=35 and...Ch. 17 - A normal distribution has mean =30kg and standard...Ch. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - Prob. 19ECh. 17 - In a normal distribution with mean =83.2 and...Ch. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - In a normal distribution with standard deviation...Ch. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution represented by...Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - Consider the normal distribution defined by Fig....Ch. 17 - A normal distribution has mean =71.5in., and the...Ch. 17 - A normal distribution has standard deviation =12.3...Ch. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Prob. 37ECh. 17 - A normal distribution has mean =500 and standard...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - In a normal distribution, what percent of the data...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 41 through 44 refer to the following:...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 45 through 48 refer to the following: As...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 49 through 52 refer to the following:...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - Exercises 53 through 56 refer to the distribution...Ch. 17 - An honest coin is tossed n=3600 times. Let the...Ch. 17 - Prob. 58ECh. 17 - Suppose that a random sample of n=7056 adults is...Ch. 17 - An honest die is rolled. If the roll comes out...Ch. 17 - A dishonest coin with probability of heads p=0.4...Ch. 17 - A dishonest coin with probability of heads p=0.75...Ch. 17 - Prob. 63ECh. 17 - Suppose that 1 out of every 10 plasma televisions...Ch. 17 - Prob. 65ECh. 17 - Prob. 66ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 68ECh. 17 - Prob. 69ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 71ECh. 17 - Percentiles. The pth percentile of a sorted data...Ch. 17 - Prob. 73ECh. 17 - Prob. 74ECh. 17 - Prob. 75ECh. 17 - Prob. 76ECh. 17 - A dishonest coin with probability of heads p=0.1...Ch. 17 - Prob. 78ECh. 17 - In American roulette there are 18 red numbers, 18...Ch. 17 - After polling a random sample of 800 voters during...
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