Question

if 20% of all manually filed returns contain errors, and 0.05% of all electronically filed returns contain errors, how much more likely is a manual filer to make an error than an electronic filer?
a. 40,000 times more likely
b. 4,000 times more likely
c. 400 times more likely
d. 40 times more likely
please select the best answer from the choices provided

Explanation:

Step1: Convert percentages to decimals

The error rate for manual filers is \(20\% = 0.2\), and for electronic filers is \(0.05\% = 0.0005\).

Step2: Calculate the ratio of error rates

To find how many times more likely a manual filer is to make an error, we divide the manual error rate by the electronic error rate: \(\frac{0.2}{0.0005}\).

Step3: Perform the division

\(\frac{0.2}{0.0005}=\frac{0.2\times10000}{0.0005\times10000}=\frac{2000}{5} = 400\). So a manual filer is 400 times more likely to make an error than an electronic filer.

Answer:

c. 400 times more likely