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

In a random sample of 67 professional actors, it was found that 36were extroverts.

(a)

Let p represent the proportion of all actors who areextroverts. 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.)
lowerlimit          
upperlimit          

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 above this interval.We are 95% confident that thetrue proportion of actors who are extroverts falls within thisinterval.     We are 5% confident that thetrue proportion of actors who are extroverts falls within thisinterval.We are 95% confident that the true proportion of actorswho are extroverts falls outside this interval.

(c)

Do you think the conditions n·p > 5 andn·q > 5 are satisfied in this problem? Explainwhy this would be an important consideration.

Yes, the conditions are satisfied. This is important because itallows us to say that p̂ is approximately binomial.No, theconditions are not satisfied. This is important because it allowsus to say that p̂ is approximatelybinomial.     Yes, the conditions aresatisfied. This is important because it allows us to say thatp̂ is approximately normal.No, the conditions are notsatisfied. This is important because it allows us to say thatp̂ is approximately normal.