For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 63 professional actors, it was found that 36 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.

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