/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 3.110 A quantitative data set has mean... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 3.110 (page 122)

A quantitative data set has mean 15and standard deviation 2. At least what percentage of the observations lie between 7and 23?

Short Answer

Expert verified

93.75%of the observations lie between7and23.

Step by step solution

01

Given information.

We have been given that ,

Mean = 15, Standard deviation = 2

We need to find the percentage of the observations that lie between7and23.

02

Simplify.

Chebyshev's Rule: At least 1001-1K2%of the data values is written kstandard deviation from the mean k>1.

Let us determine the number of standard deviation that 7and 23are from the mean.

7-meanstandarddeviation=7-152=-423-meanstandarddeviation=23-152=4

So 7and 23are 4standard deviation from the mean.

Using the Chebyshev's Rule with k=4, we know that at least,

1001-142%=1001-116%=93.75%

is within 4standard deviation from the mean.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When are the adjacent values just the minimum and maximum observation?

State pertinent properties of boxplots for symmetric, left-skewed and right-skewed distributions.

A quantitative data set has size 80. At least how many observations lie within two standard deviation of the either side?

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60miles per hour (mph) and. according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to 72mphThe following table gives the top speeds, in miles per hour, arranged in increasing order, for a sample of 35cheetahs.

The sample mean and sample standard deviation of these speeds are 59.53mphand 4.27mph, respectively. A histogram of the speeds is bell shaped.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.