Based on a Bellows survey, 48% of U.S. adults use a tax preparer to file taxes.

ID: 3330471 • Letter: B

Question

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?

Answer to question # 1)

Probability p = 48% or 0.48

Sample size n = 6

The eligibility rule of 10% is as follows:

The sample n must be not more than 10% of the population size

So suppose that if sample size is actually 10% of the population of US

then 6 = 10% of population of US

Populaton of US = 6/10% = 6/0.1 = 60

But US has more than 60 people

this implies that the population size of US is greater than 60

or in other words , 6 < 10% of Population size of US

thus the 10% rule is completely satisfied in this case

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