tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically…

tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically have a 0.05% chance of containing the same. if 2.7 million tax returns are filed each way, how many more erroneous manually filed returns will there be than erroneous electronically filed returns? a. 270,675 b. 538,650 c. 541,350 d. 269,325 please select the best answer from the choices provided

tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically have a 0.05% chance of containing the same. if 2.7 million tax returns are filed each way, how many more erroneous manually filed returns will there be than erroneous electronically filed returns? a. 270,675 b. 538,650 c. 541,350 d. 269,325 please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate number of manual - error returns

The number of manually - filed tax returns is $n_{m}=2700000$, and the error rate for manual filing is $r_{m}=20% = 0.2$. So the number of erroneous manually - filed returns is $n_{m - e}=n_{m}\times r_{m}=2700000\times0.2 = 540000$.

Step2: Calculate number of electronic - error returns

The number of electronically - filed tax returns is $n_{e}=2700000$, and the error rate for electronic filing is $r_{e}=0.05%=0.0005$. So the number of erroneous electronically - filed returns is $n_{e - e}=n_{e}\times r_{e}=2700000\times0.0005 = 1350$.

Step3: Calculate the difference

The difference between the number of erroneous manually - filed and electronically - filed returns is $d=n_{m - e}-n_{e - e}=540000 - 1350=538650$.

Answer:

B. 538,650