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Chapter 6: Q 15. (page 369)

Benford’s law Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford’s 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’t 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:

σ2=∑x-μ2Px=1-3.4412×0.301+2-3.4412×0.176+3-3.4412×0.125+4-3.4412×0.097+5-3.4412×0.079+6-3.4412×0.067+7-3.4412×0.058+8-3.4412×0.051+9-3.4412×0.046=6.060519

The standard deviation is:

σ=σ2=6.060519≈2.4618

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

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Most popular questions from this chapter

Working out Choose a person aged 19 to 25 years at random and ask, “In the past seven days, how many times did you go to an exercise or fitness center or work out?” Call the response Y for short. Based on a large sample survey, here is the probability distribution of Y

Part (a). A histogram of the probability distribution is shown. Describe its shape.

Part (b). Calculate and interpret the expected value of Y.

Ms. Hall gave her class a 10-question multiple-choice quiz.

LetX=the number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5and then add 50. Let G=the grade of a randomly chosen student in the class.

More easy quiz

a. Find the mean of G.

b. Find the range of G.

Red light! Refer to Exercise 84. Calculate and interpret P(Y≥7)

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?

a. n=10,p=0.5

b. n=40,p=0.88

c. n=100,p=0.2

d. n=100,p=0.99

e.n=1000,p=0.003

Get on the boat! Refer to Exercise 3. Find the mean of Y. Interpret this value.
See all solutions

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