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MY NOT 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 65 professional actors, it was found that 37 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate ford. (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 intervalyou have found O We are 5% confident that the true proportion of actors who arejextroverts falls within this interval. O We are 95% confident that the true propertion of actors who are extroverts falls outside this interval. O We are 95% confident that the true proportion of actors who are extroverts falls within this interval. O We are 5% confident that the true proportion of actors who are extroverts falls above this interval. (c) Do you think the conditions nip > 5 and n.q > 5 are satisfied in this problem? Explain why this would be an important consideration. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal