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?\na. 270,675\nb. 538,650\nc. 541,350\nd. 269,325\nplease 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?\na. 270,675\nb. 538,650\nc. 541,350\nd. 269,325\nplease select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate number of manual - filed errors

The number of manually - filed tax returns is $n_{m}=2.7\times10^{6}$, and the error rate is $r_{m} = 20%=0.2$. So the number of erroneous manually - filed returns is $n_{m - e}=n_{m}\times r_{m}=2.7\times10^{6}\times0.2 = 540000$.

Step2: Calculate number of electronically - filed errors

The number of electronically - filed tax returns is $n_{e}=2.7\times10^{6}$, and the error rate is $r_{e}=0.05% = 0.0005$. So the number of erroneous electronically - filed returns is $n_{e - e}=n_{e}\times r_{e}=2.7\times10^{6}\times0.0005 = 1350$.

Step3: Calculate the difference

The difference $\Delta n=n_{m - e}-n_{e - e}=540000 - 1350=538650$.

Answer:

B. 538,650