QUESTION 7 a politician, the income of a CEO, and so on. Now consider the leadin

Question

QUESTION 7 a politician, the income of a CEO, and so on. Now consider the leading digit of each number. Initially, you might think the leading digit of a randomly selected number would be equally likely to be any of the values (a discrete uniform distribution) However, evidence suggests an alternative probability distribution called Benford's Law fx(x)= RIst digit is x)= log 10(1 +-), x = 1,2, ,9 What is the probability that the leading digit is 3? (Report answer to three decimal places. Answer must be within +4 0.001 of correct value.) QUESTION 8 While reading through this year's Arkansas Democrat-Gazette newspapers, you record all numbers appearing in a news article-the number of wins by a football team, the total charitable contribution of a politician, the income of a CEO, and so on. Now consider the leading digit of each number. Initially,you might think the leading digit of a randomly selected number would be eqaly likely to be any of the values (a discrete uniform distribution). However, evidence suggests an alternative probability distribution called Benford's Law fx(x)= RIst digit is x)= log 10(1 +-), x = 1,2, ,9 What is the probability that the leading digit is at most 3? (Report answer to three decimal places. Answer must be within 0.001 of correct value.) QUESTION 9 Suppose that 23% of students who take INEG 2313 want a new copy of the textbook, and the remaining students want a used copy. Suppose INEG 2313 students begin arriving at the bookstore at some point in time On average, how many of the first 57 students want a new copy of the book? (Report answer to three decimal places. Ansver must be within +/ 0.001 of correct value) QUESTION 10 Suppose that 23% of students who take INEG 2313 want a new copy of the textbook, and the remaining students want a used copy. Suppose INEG 2313 students begin arriving at the bookstore at some point in time. What is the standard deviation of the number of new books wanted among the first 29 students? (Report answer to three decimal places. Answer must be within 0.001 of correct value.)

Explanation / Answer

Q.7 The leading digit is 3 = log10 (1 + 1/x) = log10 (1 + 1/3) = 0.125

question 8

Pr ( Leading digit is at most 3) = Pr( Leading digit = 1) + Pr( leading digit = 2) + Pr ( Leading digit = 3)

= log10 (1 + 1/1) + log10 (1 + 1/2) + log10 (1 + 1/3)

= 0.3010 + 0.1761 + 0.1249 = 0.602

Question 9 :

Expected number of students who want a new copy of the book = N * p = 57 * 0.23 = 13.11 students

Question 10 :

Standard deviation of students who want a new copy in 29 students = sqrt [N * p * (1-p)] = sqrt (29 * 0.23 * 0.77)

= 2.226 students

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