Benford's Law is a probability rule frequently used by accounting auditors to detect systematic fraud. It states that approximately 12.8% of numbers will begin with the number 2. An auditor decides to investigate a particular firm further if a sample proportion of their invoices, with the invoiced number beginning with a 2, is in the highest 0.5% of all possible sample proportions. What sample proportion will cause further investigation of the firm if a random sample of 637 invoices is selected? Express your answer in decimal form (ie not as a percentage), correct to two decimal places.

Question

Benford's Law is a probability rule frequently used by accounting auditors to detect systematic fraud. It states that approximately 12.8% of numbers will begin with the number 2.  An auditor decides to investigate a particular firm further if a sample proportion of their invoices, with the invoiced number beginning with a 2, is in the highest 0.5% of all possible sample proportions.  What sample proportion will cause further investigation of the firm if a random sample of 637 invoices is selected? Express your answer in decimal form (ie not as a percentage), correct to two decimal places.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the sample proportion that will cause further investigation, we need to determine the critical value k for the binomial distribution where the cumulative probability is 0.995. ‖ ‖ step 2 ⋮ We use the inverse binomial cumulative distribution function (CDF) with parameters $ n = 637 $ and $ p = 0.128 $ to find the smallest integer $ k $ such that $ P(X \leq k) \geq 0.995 $, where $ X $ is a binomial random variable. ‖ ‖ step 3 ⋮ Using the asksia-ll calculator, we input the inverse binomial CDF with the given parameters to find the value of $ k $. ‖ ‖ step 4 ⋮ The asksia-ll calculator provides the result for $ k $ which corresponds to the sample proportion when converted to decimal form. ‖ ∻Answer∻ ⚹ The sample proportion that will cause further investigation is [Insert the value of $ k $ divided by 637, rounded to two decimal places] ⚹ ∻Key Concept∻ ⚹Inverse Binomial CDF⚹ ∻Explanation∻ ⚹The inverse binomial CDF is used to find the critical value of $ k $ in a binomial distribution given a cumulative probability and specific parameters for $ n $ and $ p $. This value of $ k $ then helps to determine the sample proportion threshold for further investigation.⚹◊What is the formula for calculating the sample proportion given the total number of invoices and the percentage of numbers beginning with the number 2 according to Benford's Law?⍭ Generate me a similar question◊

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