For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of5260permanent dwellings on an entire reservation showed that1641were traditional hogans.

(a) Letpbe the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval forp. (Round your answer to three decimal places.)lower limitupper limit

Give a brief interpretation of the confidence interval.

99% of all confidence intervals would include the true proportion of traditional hogans.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans

1% of all confidence intervals would include the true proportion of traditional hogans.

99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

(c) Do you think thatnp>5 andnq>5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.