The chance of an IRS audit for a tax return reporting more than 25,000 in income is about 2% per year a. give the distribution of X. X∼B(__,__) b. how many audits are expected in a 20 year period? c. find the probability that a person is not audited at all. d. find the probability that a person is all the dead more than twice.

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The chance of an IRS audit for a tax return reporting more than 25,000 in income is about 2% per year  a. give the distribution of X. X∼B(__,__)  b. how many audits are expected in a 20 year period?  c. find the probability that a person is not audited at all.  d. find the probability that a person is all the dead more than twice.

usaho4w · Accepted Answer

Step 1  Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved  (a) Determine the distribution of X.  The distribution of X is determined below as follows:  Let X denotes the number of audits a person with the income more than 25,000 which follows binomial distribution with the probability of success 0.02 and the number of years selected is 20.  That is, n=20,p=0.02,q=0.98(=1−0.02).  Therefore,  X∼B(20,0.02)  Step 2  (b) Obtain the expected number of audits in a 20 year period.  The expected number of audits in a 20 year period is obtained below as follows:  The required value is,  E(x)=np  =20×0.02  =0.40  The expected number of audits in a 20 year period is 0.40.  Step 3  (c) Obtain the probability that a person is not audited at all.  The probability that a person is not audited at all is obtained below as follows:  The required probability  Use Excel to obtain the probability value for x equals 0.  Follow the instruction to obtain the P-value:  1. Open EXCEL  2.Go to Formula bar.  3. In formula bar enter the function as“=BINOMDIST”  4. Enter the number of success as 0.  5. Enter the Trails as 20  6. Enter the probability as 0.02  7. Enter the cumulative as False.  8. Click enter  EXCEL output:  From the Excel output, the P-value is 0.6676  The probability that a person is not audited at all is 0.6676.

braodagxj · Accepted Answer

Step 1 a) In words, dene the Random Variable X. Solution: X = number of audits a person with income over $25,000 per annum has in a 20 year period. b) List the values that X may take on. Solution: S={0, 1, 2,⋯, 19, 20} c) Give the distribution of X. Solution: X∼B(20, 0.02) or we could use the mean value calculated below and approximate with the Poisson distribution X∼P(0.4) d) How many audits are expected in a 20 year period? Solution: (0.98)20 or binom pdf(20, 0.02, 0)=0.668 or poisson pdf(0.4, 0)=0.670

karton · Accepted Answer

Step 1 Given: n=20 p=0.02 X=the number of audits a person with income over $25,000 per annum has in a 20 year period and the values of X are 0, 1, 2, ⋯, 19, 20 Here X follows the Binomial distribution with the parameters n=20 and p=0.02 X∼Binomial(n=20, p=0.02) a) The number of audits are expected in a 20-year period is Mean, μ=np=20×0.02=0.4 b) Standard deviation, SD=np(1−p)=20×0.02(1−0.02)=0.6261 The standard deviation is 0.6261 c) The probability function of Binomial Distribution is given by P(x=x)=((n),(x))px(1−p)n−x So probability of being audited troice is P(x=2)=((20),(2))(0.02)2(1−0.02)20−2 =0.0528 P(x=2)=0.0528 d) P(x&amp;gt;3)=1−p(x≤3) =1−∑x=03((20),(x))(0.02)x(1−0.02)20−x =1−0.9994 =0.0006 P(x&amp;gt;3)=0.0006

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