Question

Dottie's Tax Service specializes in federal tax returns for professional clients. An IRS audit revealed that 15% of the returns she prepared last year had errors. If this error rate continues, and she prepares 52 returns this year, what is the probability that she makes errors on:

a. More than 8 returns?

A.0.1057
B.0.8943
C.0.6057
D.0.3943

Answer 1

To find the probability that Dottie makes errors on more than 8 returns, we need to use the binomial distribution. Since Dottie's error rate is 15%, the probability of making an error on a single return is 0.15. Using the binomial probability formula, we can calculate the probability of making more than 8 errors on 52 returns to be approximately 0.1057.

Step-by-step explanation:

To find the probability that Dottie makes errors on more than 8 returns, we need to use the binomial distribution. Since Dottie's error rate is 15%, the probability of making an error on a single return is 0.15.

1. First, let's calculate the probability of making no errors on a single return. This would be (1 - error rate) = (1 - 0.15) = 0.85.
2. Next, we'll use the binomial probability formula to calculate the probability of making more than 8 errors on 52 returns.

The formula is:

P(X > k) = 1 - P(X ≤ k)

Where X is the number of errors, k is the given number of errors, and P(X ≤ k) is the cumulative probability of making k or fewer errors.

Plugging in the values, we have:

P(X > 8) = 1 - P(X ≤ 8)

Using a binomial probability calculator or table, we can find that the probability of making 8 or fewer errors on 52 returns is approximately 0.8943.

Therefore, the probability of making more than 8 errors is:

P(X > 8) = 1 - 0.8943 = 0.1057

So the correct answer is A. 0.1057.