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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
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 55 professional actors, it was found that 45 were extroverts. (a) Let p represent the proportion of ali actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) : (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 confidence interval you have found. 0 We are 95% condent that the true proportion of actors who are extroverts falls outside this interval. 0 We are 95% condent that the true proportion of actors who are extroverts falls within this interval. 0 We are 5% condent that the true proportion of actors who are extrovei'ts falls within this interval. 0 We are 5% condent that the true proportion of actors who are extroverts falls above this intenr'al. (c) Do you think the conditions 11-}: :> 5 and n-q :> 5 are sab'sed in this problem? Explain why this would be an important consideration. 0 No, the conditions are not satised. This is important because it allows us to say that :3 is approximately binomial. 0 Yes, the conditions are satised. This is important because it ailows us to say that is approximately binomial. O No, the conditions are not satised. This is important because it allows us to say that p is approximately normal. 0 Yes, the conditions are satised. This is important because it ailows us to say that is approximately normai
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