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 of64professional actors, it was found that39were extroverts.

(a)Letprepresent the proportion of all actors who are extroverts.Find a point estimate forp. (Round your answer to four decimal places.)____

(b)Find a 95% confidence interval forp. (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 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.____

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.____

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.____

(c)Do you think the conditionsnp>5 andnq>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 thatpis approximately binomial._____

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.____

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.____

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.____