Question

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

Explanation:

Step1: Calculate errors in manual returns

Total manual returns: \(2.7\) million \( = 2700000\). Error rate: \(20\% = 0.2\).
Errors in manual: \(2700000\times0.2 = 540000\).

Step2: Calculate errors in electronic returns

Error rate for electronic: \(0.05\% = 0.0005\).
Errors in electronic: \(2700000\times0.0005 = 1350\).

Step3: Find the difference

Difference: \(540000 - 1350 = 538650\).

Answer:

b. 538,650