Question

In the current tax year, IRS estimates that 5% of the many high net worth individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let's suppose that a thorough IRS audit will uncover them. (a) If at random 100 such tax returns are audited, what is the probability that exactly 5 fraudulent returns will be uncovered? Ans: (b) If at random 200 such tax returns are audited, what is the probability that at least 15 fraudulent returns will be uncovered? Ans: (c) If at random 140 such tax returns are audited, what is the probability that at the most 11 fraudulent returns will be uncovered? Ans:

          In the current tax year, IRS estimates that 5% of the many high net worth individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let's suppose that a thorough IRS audit will uncover them.

(a) If at random 100 such tax returns are audited, what is the probability that exactly 5 fraudulent returns will be uncovered?

Ans:

(b) If at random 200 such tax returns are audited, what is the probability that at least 15 fraudulent returns will be uncovered?

Ans:

(c) If at random 140 such tax returns are audited, what is the probability that at the most 11 fraudulent returns will be uncovered?

Ans:

Show more…

In the current tax year, IRS estimates that 5% of the many high net worth individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let's suppose that a thorough IRS audit will uncover them.

(a) If at random 100 such tax returns are audited, what is the probability that exactly 5 fraudulent returns will be uncovered?

Ans:

(b) If at random 200 such tax returns are audited, what is the probability that at least 15 fraudulent returns will be uncovered?

Ans:

(c) If at random 140 such tax returns are audited, what is the probability that at the most 11 fraudulent returns will be uncovered?

Ans:

Added by Guillermo F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

11/10/2021

Step 1

Using the binomial distribution formula, we have: \[ P(X = 5) = \binom{100}{5} \times (0.05)^5 \times (0.95)^{95} \] Show more…

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In the current tax year, IRS estimates that 5% of the many high net worth individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let's suppose that a thorough IRS audit will uncover them. (a) If at random 100 such tax returns are audited, what is the probability that exactly 5 fraudulent returns will be uncovered? Ans: (b) If at random 200 such tax returns are audited, what is the probability that at least 15 fraudulent returns will be uncovered? Ans: (c) If at random 140 such tax returns are audited, what is the probability that at the most 11 fraudulent returns will be uncovered? Ans:

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Transcript

00:01 Hi, i'm david and i'm here to have you answering your question.

00:04 Now let me bring up your question here.

00:07 In this question we will recall about the binomial distribution.

00:12 Let me remind you that if we have an x followed by the binomial and p and then the probability the x equal to k, you equal to the n2 sk, p power k times 1 minus p power n minus k and in this question here we are given that the 5 % on the money high net worth individual tax return would be fraudulent means then the probability of the fraud it will equal to the 5 % will be 0 .05 and if we call the x equal to the x equal to the number of the front text return and therefore x will follow by the polynomial when the n equal to depending on the question here so equal to n and then p u equal to the zp.

01:19 0 5 now in the part a we're given n equal to a p equal to 0 .05.

01:34 The question asks us, when is the probability that exactly 5 fratern and return will be uncovered? it means that i want to find the probability of the x equal to 5.

01:48 And if we use the formula here, we should get the 100, we choose 5, 0 .0 5, power 5 and then 1 minus 0 .05 will be 0 .95 power of the 95.

02:06 If we compute this one, we should get the answer.

02:10 So let me do it for you.

02:13 Now probability success is 0 .05 and then number trial equal to 100.

02:23 Now number success will be 5.

02:27 So get equal to 0 .18.

02:32 0 0 and this will be the answer for the a...

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