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
To find the answer, we need to compare the proportion of errors in manually filed returns to the proportion of errors in electronically filed returns.
The proportion of errors in manually filed returns is 20% = 0.2.
The proportion of errors in electronically filed returns is 0.05% = 0.0005.
To find out how much more likely manual filers are to make an error than electronic filers, we need to compare these two proportions.
The proportion of errors in manual filings is 0.2 / 0.0005 = 400.
Therefore, a manual filer is 400 times more likely to make an error than an electronic filer.
The answer is c. 400 times more likely.
To determine how much more likely a manual filer is to make an error than an electronic filer, we need to compare the error rates of both types of filing.
Let's assume we have 1,000 returns for simplicity.
For manual filing:
- 20% of all manually filed returns contain errors, which means 20% of 1,000 = 0.20 * 1,000 = 200 returns contain errors.
For electronic filing:
- 0.05% of all electronically filed returns contain errors, which means 0.05% of 1,000 = 0.0005 * 1,000 = 0.5 returns contain errors.
To calculate how much more likely a manual filer is to make an error than an electronic filer, we can divide the number of errors for manual filing by the number of errors for electronic filing.
So, 200 / 0.5 = 400.
Therefore, a manual filer is 400 times more likely to make an error than an electronic filer.
Hence, the answer is c. 400 times more likely.