a. Explanation Calculation: The Benford’s law states that certain digits have more chance to occur as the first significant digit than other digits. A sample of 743 students is randomly selected to write down a six-digit number at random. The table summarizes the occurrence of the first digit number and its frequency. Frequency: The frequency is the number of times each observation falls in a category. Relative frequency: The relative frequency of a particular category is the proportion of observations that fall on each category. That is, Relative frequency = Frequency Total number of observations in the data set Relative frequency distribution: A frequency distribution that includes relative frequencies is called relative frequency distribution. The relative frequency of each category is obtained by converting the percentages into probabilities. [ Relative frequency for the digit 1 ] = [ Frequency Total sample size ] = 109 743 = 0.147 Similarly, the other probabilities are obtained, and the relative frequency distribution is as follows: First Digit Number of Occurrences Relative Frequency 1 109 0 (b) To determine Calculate E ( x ) and interpret the result. (c) To determine Write a practical interpretation of E ( x ) , if possible.

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 4, Problem 137ACB

To determine

Construct a probability distribution for the first significant digit x.

(b)

To determine

Calculate E(x) and interpret the result.

(c)

To determine

Write a practical interpretation of E(x), if possible.

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Chapter 4, Problem 136ACB

Chapter 4, Problem 138ACB

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Construct a probability distribution for the first significant digit x .

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Construct a probability distribution for the first significant digit x.

Calculate E(x) and interpret the result.

Write a practical interpretation of E(x), if possible.

Want to see the full answer?

Chapter 4 Solutions