For this problem, carry at least four digits after the decimalin your calculations. Answers may vary slightly due to rounding. Ina random sample of 61 professional actors, it was found that 45were extroverts. (a) Let p represent the proportion of all actorswho are extroverts. Find point estimates for p and q. (Round youranswer to four decimal places.) p̂ = q̂ = (b) Find a 95% confidenceinterval for p. (Round your answers to two decimal places.) Findthe maximal margin of error. (Round your answer to two decimalplaces.) E = Report the bounds from the 95% confidence interval forp. (Round your answers to two decimal places.) lower limit upperlimit Give a brief interpretation of the meaning of the confidenceinterval you have found. We are 5% confident that the trueproportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who areextroverts falls outside this interval. We are 95% confident thatthe true proportion of actors who are extroverts falls within thisinterval. We are 5% confident that the true proportion of actorswho are extroverts falls within this interval. (c) Do you think theconditions np > 5 and nq > 5 are satisfied in this problem?Explain why this would be an important consideration. Yes, theconditions are satisfied. This is important because it allows us tosay that p̂ is approximately normal. No, the conditions are notsatisfied. This is important because it allows us to say that p̂ isapproximately normal. No, the conditions are not satisfied. This isimportant because it allows us to say that p̂ is approximatelybinomial. Yes, the conditions are satisfied. This is importantbecause it allows us to say that p̂ is approximately binomial.