Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 3.122 (page 123)


The data set has mean15and standard deviation 2. Approximately what percentage of the observations lie between 13and 17?

Short Answer

Expert verified

The percentage of the observations lie between 13and 17is68%

Step by step solution

01

Step 1:Given information

We are given that data set has mean15and standard deviation2 .

02

Simplify

We will use empirical rule, to determine approximate values for the percentage of observations between13and17.

We are given that μ=15andσ=2, where μis mean and σis standard deviation.

Also , the given interval (13,17)will be formed by adding and subtracting standard deviations from the mean.We will check for different values of k.

So using the value of mean and standard deviation , we get , μ-kσ,μ+kσ=(13,17)⇒k=1

By empirical rule , Pμ-σ<X<μ+σ≈0.68where Xis given interval.

So percentage is68%

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences, The recommended dietary allowance (RDA) of iron for adult females under the age of 51is 18milligrams (mg) per day. The iron intakes during a 24-hour period for a random sample of45 adult females under the age of 51have a mean of 14.7mgand standard deviation of 3.1mg.

a. Construct a graph .
b. Apply Chebyshev's rule with k=2 to make pertinent statements about the observations in the sample.
c. Repeat part (b) with k=3.

Augusta National Golf Course. Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is 132.0yd. In this context. is the number 132.0a parameter or a statistic? Explain your answer.

A quantitative data set of size150has mean 35 and standard deviation4. At least how many observations lie between 23and 47?

Discuss the pros and cons of Chebyshev's rule.

Fill in the following blanks.

(a) A standardized variable always has mean _____ and standard deviation _______ .

(b) The z-score corresponding to an observed value of a variable tells you ______ .

(c) A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

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.

Sign-up for free