Question

According to the internal revenue service, 75% of all tax returns lead to a refund. a random sample of 100 tax returns is taken. what is the mean of the distribution of the sample proportion of returns leading to refunds?

Answer 1

The mean of the distribution of the sample proportion of tax returns leading to refunds is 75, calculated by multiplying the sample size (100) by the probability of getting a refund (0.75).

Step-by-step explanation:

The student's question pertains to finding the mean of the distribution of the sample proportion of tax returns that lead to a refund. Given that the Internal Revenue Service states 75% of all tax returns lead to a refund, and a random sample of 100 tax returns is considered, we would expect the proportion in the sample to be close to the population proportion.

So, the mean of the distribution of sample proportions can be calculated using the formula for the mean of a binomial distribution, which is np, where n is the sample size, and p is the probability of success (in this case, getting a refund).

Here, n is 100 (the sample size), and p is 0.75 (the probability of a refund). Therefore, the mean of the sample distribution would be 100 * 0.75 = 75. This means that in our sample of 100 tax returns, we would expect on average that 75 of them will lead to a refund.