In a random sample of 65 professional actors, it was found that 39 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b)Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit_______ upper limit_______ Give a brief interpretation of the meaning of the confidence interval you have found.

(A)We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

(B) We are 95% confident that the true proportion of actors who are extroverts falls within this interval. (C) We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

(D) We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

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

(A) Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial.

(B) No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial.

(C) No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal.

(D) Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal.