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 61 professional actors, it was found that 40 were extroverts. (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 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 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.

(c)

Do you think the conditions np> 5 and nq> 5 are satisfied in this problem? Explain why this would be an important consideration.

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.

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