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?
○ 40,000 times more likely
○ 4,000 times more likely
○ 400 times more likely
○ 40 times more likely

Explanation:

Step1: Convert percentages to decimals

20% as a decimal is $0.2$, and 0.05% as a decimal is $0.0005$ (since $0.05\%=\frac{0.05}{100}=0.0005$).

Step2: Divide the manual error rate by the electronic error rate

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: Calculate the division

$\frac{0.2}{0.0005}=\frac{0.2\times10000}{0.0005\times10000}=\frac{2000}{5} = 400$.

Answer:

400 times more likely (the option: 400 times more likely)