Suppose that an IRS examiner correctly detects and flags 90% of all erroneous returns that he reviews. In addition, he mistakenly flags 2% of correct returns that he reviews. Suppose that about 20% of the tax returns he reviews contain errors.

(a) What proportion of tax returns he reviews are flagged?
(b) What proportion of tax returns he flagged actually contain errors?

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alasharjamal1 alasharjamal1 · Answer 1 · 2020-02-10T15:35:55+01:00

Answer:Proportion Of Flags=19.6%

part b: Proportion of flagged returns containing error =91.8%

Step-by-step explanation: The examiner flags the 90% of the erroneous returns so if for example he get 50 erroneous returns he will flag

50*90/100=45

of them

Similarly if he gets 100 correct returns, he will flag

100*2/100=2

of those a/c to the question

So as it is mentioned that the returns he reviews contain 20% erroneous returns so the rest of the returns i.e. 80% will be correct.

Hence he will flag 90% of the erroneous and 2% of the correct ones

[tex]Proportion Of Flags=20\frac{90}{100} +80\frac{2}{100} \\[/tex]

Proportion Of Flags=19.6%

part b

Now we have to find the ratio of erroneous returns flagged to the total number of flags which can be found by

[tex]Proportion2=\frac{20*90/100}{19.6}[/tex]

Proportion2=0.918

in percentage

Proportion2=91.8%