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 of61professional actors, it was found that37were 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

(c) 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 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 within this interval.

(d) 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.

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 binomial.

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