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

In a random sample of 63 professional actors, it was found that 39were extroverts.

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


(b) Find a 95% 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 5% confident that the true proportion of actors who areextroverts falls within this interval.We are 95% confident that thetrue proportion of actors who are extroverts falls outside thisinterval.    We are 5% confident that the trueproportion of actors who are extroverts falls above thisinterval.We are 95% confident that the true proportion of actorswho are extroverts 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.No, theconditions are not satisfied. This is important because it allowsus to say that p? is approximatelynormal.    Yes, the conditions are satisfied.This is important because it allows us to say that p? isapproximately normal.No, the conditions are not satisfied. This isimportant because it allows us to say that p? isapproximately binomial.