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
To find the difference in erroneous returns filed manually and electronically, we need to calculate the number of erroneous returns for each method.
For manually filed returns, the chance of error is 20%, so the number of erroneous returns is 20% of 2.7 million: 0.2 * 2,700,000 = 540,000.
For electronically filed returns, the chance of error is 0.05%, so the number of erroneous returns is 0.05% of 2.7 million: 0.0005 * 2,700,000 = 1,350.
Therefore, the difference is 540,000 - 1,350 = 538,650.
Therefore, the answer is (b) 538,650.
To find the difference in the number of erroneous manually filed returns and electronically filed returns, we need to calculate the number of errors for each method and subtract them.
For manually filed returns:
Number of tax returns filed manually = 2.7 million
Chance of errors in manually filed returns = 20% = 0.20
Number of erroneous manually filed returns = 2.7 million * 0.20 = 540,000
For electronically filed returns:
Number of tax returns filed electronically = 2.7 million
Chance of errors in electronically filed returns = 0.05% = 0.0005
Number of erroneous electronically filed returns = 2.7 million * 0.0005 = 1,350
Difference in erroneous returns = Number of erroneous manually filed returns - Number of erroneous electronically filed returns
= 540,000 - 1,350
= 538,650
Therefore, the correct answer is b. 538,650