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 62 professional actors, it was found that 42 were extroverts. LA USE SALT (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. We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. 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 no > 5 are satisfied in this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. Need Help? Rese Witch 4. [-/0.2 Points] DETAILS BBUNDERSTAT12 7.3.012 MI.S. 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 540 judges, it was found that 283 were introverts. USE SALT (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% 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. We are 99% confident that the tru proportion of judges who are introverts falls within this interval. We are 99% confident that the true proportion of ju introverts falls outside this interval. We are 1% confident that the true proportion of judges who are introverts falls above this interval, We are 1% confident that the true proportion of judges who are introverts falls within this interval