`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. `

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Answer from Sia

Posted 6 months ago

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.

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