For this problem, carry at least four digits after the decimalin your calculations. Answers may vary slightly due torounding.

In a random sample of 520 judges, it was found that 291 wereintroverts.

(a) Let p represent the proportion of all judges whoare introverts. Find a point estimate for p. (Round youranswer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round youranswers to two decimal places.)

lower limit
upper limit

Give a brief interpretation of the meaning of the confidenceinterval you have found.

We are 99% confident that the true proportion of judges who areintroverts falls outside this interval.We are 1% confident that thetrue proportion of judges who are introverts falls above thisinterval.    We are 99% confident that the trueproportion of judges who are introverts falls within thisinterval.We are 1% confident that the true proportion of judges whoare introverts falls within this interval.

(c) Do you think the conditions np > 5 and nq> 5 are satisfied in this problem? Explain why this would be animportant consideration.

Yes, the conditions are satisfied. This is important because itallows us to say that p? is approximately binomial.Yes,the conditions are satisfied. This is important because it allowsus to say that p? is approximatelynormal.    No, the conditions are notsatisfied. This is important because it allows us to say thatp? is approximately binomial.No, the conditions are notsatisfied. This is important because it allows us to say thatp? is approximately normal.