/*! 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 77 Describe the 68-95-99.7 Rule.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 77

Describe the 68-95-99.7 Rule.

Short Answer

Expert verified
The 68-95-99.7 Rule, or Empirical Rule, states that in a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step by step solution

01

Understand what a Normal Distribution is

A Normal Distribution, also known as a Gaussian Distribution, is a type of continuous probability distribution for a real-valued random variable. In a normal distribution, the data is symmetrically distributed with no skew. The mean, median, and mode of a normal distribution are equal. The shape of a normal distribution is determined by the mean and the standard deviation.
02

Define Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. It is represented by the Greek letter sigma \(\sigma\)
03

Describe the 68-95-99.7 Rule

The empirical rule, or the 68-95-99.7 rule, states that for a given dataset with a normal distribution: \n\n 1. 68% of data falls within the first standard deviation from the mean. \n 2. 95% falls within the second standard deviation. \n 3. Lastly, 99.7% falls within the third standard deviation. \n\n This rule is empirical because it's based on repeated and varied experimental results, rather than being a product of pure mathematical derivation.

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

Group members should consult a current almanac or the Internet and select intriguing data. The group's function is to use statistics to tell a story. Once "intriguing" data are identified, as a group a. Summarize the data. Use words, frequency distributions, and graphic displays. b. Compute measures of central tendency and dispersion, using these statistics to discuss the data.

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20.Find the score that is \(2 \frac{1}{2}\) standard deviations above the mean.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I scored in the 50 th percentile on a standardized test, so my score is the median.

What does a \(z\)-score measure?

If you score in the 83rd percentile, what does this mean?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

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.