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
a
b
c
d

Explanation:

Step1: Identify the error rates

Let the error rate for manual filers be \( P(M) = 20\% = 0.2 \) and for electronic filers be \( P(E) = 0.05\% = 0.0005 \).

Step2: Calculate the ratio of error rates

To find how many times more likely a manual filer is to make an error than an electronic filer, we calculate the ratio \( \frac{P(M)}{P(E)} \).

Substitute the values: \( \frac{0.2}{0.0005} = \frac{0.2}{5\times10^{-4}} = \frac{0.2\times10^{4}}{5} = \frac{2000}{5} = 400 \).

So the manual filer is 400 times more likely to make an error than the electronic filer.

Answer:

c. 400 times more likely