Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q.5.24

Expert-verified

Introductory Statistics

Found in: Page 348

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as $X ~ U (1.5, 4.5)$ .
What is the $90^{t h}$ percentile of square footage for homes?

The value of the $90^{t h}$ percentile of square footage for homes is $4.2$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Table,

Sample mean = 2.50

Standard deviation = 0.8302

Step 2: Solution

Here, we need to find the probability density function or height of the $X ~ U (1.5, 4.5)$ ,

$f (x) = height$

$= \frac{1}{4.5 - 1.5}$

$= \frac{1}{3}$

So, the $90^{th}$ percentile will be,

$P (x < k) = base \times height$

$0.90 = (k - 1.5) (\frac{1}{3})$

$(k - 1.5) = 0.90 \times 3$

$k = 2.7 + 1.5$

$k = 4.2$

Most popular questions for Math Textbooks

A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?

$f (x)$ for a continuous probability function is $1 5$ , and the function is restricted to $0 \leq x \leq 5$ . What is $P (x < 0)$ ?

According to the American Red Cross, about one out of nine people in the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution.

a. If $100$ people arrive, how many on average would be expected to have Type B blood?

b. What is the probability that over $10$ people out of these 100 have type B blood?

c. What is the probability that more than $20$ people arrive before a person with type B blood is found?

Use the following information to answer the next seven exercises. A distribution is given as $X ~ E x p (0.75)$ . Which is larger, the mean or the median?

Use the following information to answer the next eight exercises. A distribution is given as $X ~ U (0, 12)$ .

What is a? What does it represent?

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free