/*! 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} Problem 61 Under what assumptions are the e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 61

Under what assumptions are the estimates in the empirical rule exact?

Short Answer

Expert verified
The estimates in the empirical rule are exact under the following assumptions: (1) the data is normally distributed, (2) the data set has a mean and standard deviation, and (3) the data is continuous. If these assumptions are not met, the empirical rule may not provide accurate estimates.

Step by step solution

01

Assumption 1: The data is normally distributed.

The empirical rule only applies to normally distributed data. A normal distribution is a bell-shaped curve where most of the data points cluster around the mean. If the data is not normally distributed, the empirical rule's estimates would not be exact.
02

Assumption 2: Population or sample has a mean and standard deviation

The empirical rule calculations require that the data set has a mean (average) and standard deviation (a measure of variance). If the data set does not have these values or they're not representative of the data set, the empirical rule's accuracy may be diminished.
03

Assumption 3: The data is continuous.

The normal distribution assumes that the data points can take any value within a specific range. This means that the data is continuous, and there are no gaps between data points. If the data is discrete, the empirical rule's estimates may not be exact. In summary, the estimates in the empirical rule are exact under the assumptions that the data is normally distributed, has a mean and standard deviation, and is continuous. If these assumptions do not hold, the empirical rule may not provide accurate estimates for the proportion of data within the specified standard deviations 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

In a certain set of scores, the median occurs more often than any other score. It follows that (A) The median and mean are equal. (B) The mean and mode are equal. (C) The mode and median are equal. (D) The mean, mode, and median are all equal.

Pastimes A survey of all the students in your school yields the following probability distribution, where \(X\) is the number of movies that a selected student has seen in the past week: \begin{tabular}{|r|c|c|c|c|c|} \hline Number of Movies & 0 & 1 & 2 & 3 & 4 \\ \hline Probability & \(.5\) & \(.1\) & \(.2\) & \(.1\) & \(.1\) \\ \hline \end{tabular} Compute the expected value \(\mu\) and the standard deviation \(\sigma\) of \(X\). (Round answers to two decimal places.) For what percentage of students is \(X\) within two standard deviations of \(\mu\) ?

A survey of 52 U.S. supermarkets yielded the following relative frequency table, where \(X\) is the number of checkout lanes at a randomly chosen supermarket. \({ }^{23}\) $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & .01 & .04 & .04 & .08 & .10 & .15 & .25 & .20 & .08 & .05 \\ \hline \end{array} $$ a. Compute \(\mu=E(X)\) and interpret the result. HINT [See Example 3.] b. Which is larger, \(P(X<\mu)\) or \(P(X>\mu)\) ? Interpret the result.

\- Find an algebraic formula for the sample standard deviation of a sample \(\\{x, y\\}\) of two scores \((x \leq y)\).

Your friend Charlesworth claims that the median of a collection of data is always close to the mean. Is he correct? If so, say why; if not, give an example to prove him wrong.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

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.