/*! 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 15. Benford鈥檚 law Exercise 9 descr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q 15. (page 369)

Benford鈥檚 law Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford鈥檚 law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can鈥檛 be 0). From Exercise 9, E(X)=3.441. Find the standard deviation of X. Interpret this value.

Short Answer

Expert verified

The standard deviation is 2.4618.

Step by step solution

01

Step 1. Given information.

The given information is:

02

Step 2. Find and interpret the standard deviation of X.

The given mean is 3.441.

The predicted value of the squared departure from the mean is known as the variance:

蟽2=鈭�x-渭2Px=1-3.4412脳0.301+2-3.4412脳0.176+3-3.4412脳0.125+4-3.4412脳0.097+5-3.4412脳0.079+6-3.4412脳0.067+7-3.4412脳0.058+8-3.4412脳0.051+9-3.4412脳0.046=6.060519

The standard deviation is:

蟽=蟽2=6.060519鈮�2.4618

We can see that on an average the first digit will vary from a mean of 3.441 by 2.4618.

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

Skee BallAna is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana鈥檚 score Xon a randomly selected roll of the ball is shown here. From Exercise 8, 渭X=23.8.

(a) Find the median of X.

(b) Compare the mean and median. Explain why this relationship makes sense based on the probability distribution.

Victoria parks her car at the same garage every time she goes to work. Because she stays at work for different lengths of time each day, the fee the parking garage charges on a randomly selected day is a random variable, G. The table gives the probability distribution of G.You can check that 渭G=\(14and 蟽G=\)2.74.

In addition to the garage鈥檚 fee, the city charges a $3use tax each time Victoria parks her car. Let T=the total amount of money she pays on a randomly selected day.

a. Make a graph of the probability distribution of T. Describe its shape.

b. Find and interpret 渭T.

c. Calculate and interpret 蟽T.

Ladies Home Journal magazine reported that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Assume that this claim is true. Suppose 12 dog owners are selected at random. Let X= the number of owners who greet their dogs first.

a. Explain why it is reasonable to use the binomial distribution for probability calculations involving X.

b. Find the probability that exactly 6 owners in the sample greet their dogs first when returning home from work.

c. In fact, only 4 of the owners in the sample greeted their dogs first. Does this give convincing evidence against the Ladies Home Journal claim? Calculate P(X鈮�4) and use the result to support your answer.

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

Working outExercise 10 described a large sample survey that asked a sample of people aged 19 to 25 years, 鈥淚n the past seven days, how many times did you go to an exercise or fitness center or work out?鈥� The response Y for a randomly selected survey respondent has the probability distribution shown here. From Exercise 10, E(Y)=1.03. Find the standard deviation of Y. Interpret this value.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.