STA2023 Lab 2 Binomial Model

We are required to cover the binomial model in this course. Unfortunately, our textbook covers this model, but has very few homework problems associated with using the model. Therefore, the following lab focuses on using the binomial model. Please print and fill out this document. Then use your answers to answer the questions on the "quiz" located in the "Lab #2" Assignment I will post solutions after the due date.

(Round your answers to 4 decimal places) Taxes. Based on a Bellows survey, 48% of U.S. adults use a tax preparer to file taxes. Select 6 U.S. adults at random.

1. Since we are taking a sample of 6 U.S. adults, we are not picking people with replacement. So, technically, we do not have true  independence (even though we are picking at random). So theoretically, every time we pick a person, the probability that the next person uses a tax preparer should change. However, if the sample size is small enough in comparison with the population size, the differences in the probability of "success" for each person is negligible. In that case, we can assume independence, and so we can assume that the probability of "success" stays the same for each randomly chosen person. In order to assume independence, we check the 10% condition.

Can we assume independence for the 6 selected U.S. adults? Check by showing the 10% condition is satisfied.

2. Find the probability that, out of the 6 people chosen, exactly 5 people use a tax preparer.

3. Find the probability that, out of the 6 people chosen, 4 or 5 people use a tax preparer.

4. Find the probability that, out of the 6 people chosen, at most 4 people use a tax preparer.

5. Out of the 6 people chosen, how many do we expect to use a tax preparer?

6. What is the standard deviation for the number of people who use a tax preparer?

7. If we select 1000 U.S. adults at random, what is the probability that at least 500 of them use a tax preparer?