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 61 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 ,9. (Round your answer to four decimal places.) :J {b} Find a 95% condence interval for p. {Round your answers to two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the condence interval you have found. Q We are 95% confident that the true proportion of actors who are extroverts falls within this interval. O We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. Q We are 5% condent that the true proportion of actors who are extroverts falls within this Interval. Q We are 5% condent that the true proportion of actors who are extroverts falls above this interval. (c) Do you think the conditions n-p :v 5 and my 5 5 are satised in this problem? Explain why this would be an important consideration. 0 Yes, the conditions are satisfied. This Is important because it allows us to say that}?! Is approximately normal. 0 Yes, the conditions are satisfied. This Is important because it allows us to say thatjil Is approximately binomial. O No, the conditions are not satised. This is important because it allows us to say that ii is approximately nOrmal. O No, the conditions are not satised. This is important because it allows us to say that ii is approximately binomial