/*! 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 73 Briefly explain the empirical ru... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 73

Briefly explain the empirical rule. To what kind of distribution is it applied?

Short Answer

Expert verified
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, nearly all data will fall within three standard deviations of the mean. It applies only to a normal (Gaussian) distribution, which must be continuous, unimodal, and symmetric around the mean.

Step by step solution

01

Definition of the Empirical Rule

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean.
02

Understanding Standard Deviations

A standard deviation is a measurement of how spread out numbers are in a set of data. It's calculated as the square root of the variance. The variance is the average of the squared differences from the mean. In other words, standard deviation tells us how much our data deviates from the average on average.
03

The Normal Distribution

The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean. It shows that data near the mean are more frequent in occurrence than data far from the mean. In other words, a graph of the normal distribution forms a bell-shaped curve.
04

Application of the Empirical Rule

The empirical rule can only be applied to a normal distribution (bell-shaped curve), and only if the data is continuous, unimodal (only one mode), and symmetric around the mean. It can't be used with any other distribution.

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

A sample of 3000 observations has a mean of 82 and a standard deviation of 16 . Using the empirical rule, find what percentage of the observations fall in the intervals \(\bar{x} \pm 1 s, \bar{x} \pm 2 s\), and \(\bar{x} \pm 3 s\).

Answer the following questions a. The total weight of all pieces of luggage loaded onto an airplane is 12,372 pounds, which works out to be an average of \(51.55\) pounds per piece. How many pieces of luggage are on the plane? b. A group of seven friends, having just gotten back a chemistry exam, discuss their scores. Six of the students reveal that they received grades of \(81,75,93,88,82\), and 85, respectively, but the seventh student is reluctant to say what grade she received. After some calculation she announces that the group averaged 81 on the exam. What is her score?

The mean age of six persons is 46 years. The ages of five of these six persons are \(57,39,44,51\), and 37 years, respectively. Find the age of the sixth person.

Melissa's grade in her math class is determined by three 100 -point tests and a 200 -point final exam. To determine the grade for a student in this class, the instructor will add the four scores together and divide this sum by 5 to obtain a percentage. This percentage must be at least 80 for a grade of \(\mathrm{B}\). If Melissa's three test scores are 75,69 , and 87 , what is the minimum score she needs on the final exam to obtain a B grade?

According to Fair Isaac, "The Median FICO (Credit) Score in the U.S. is 723" (The Credit Scoring Site, 2009). Suppose the following data represent the credit scores of 22 randomly selected loan applicants. \(\begin{array}{lllllllllll}494 & 728 & 468 & 533 & 747 & 639 & 430 & 690 & 604 & 422 & 356 \\ 805 & 749 & 600 & 797 & 702 & 628 & 625 & 617 & 647 & 772 & 572\end{array}\) a. Calculate the values of the three quartiles and the interquartile range. Where does the value 617 fall in relation to these quartiles? b. Find the approximate value of the 30 th percentile. Give a brief interpretation of this percentile. c. Calculate the percentile rank of 533 . Give a brief interpretation of this percentile rank.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.