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 of516judges, it was found that283were introverts.

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

(b) Find a 99% 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.

a)We are 99% confident that the true proportion of judges who are introverts falls within this interval.

b)We are 1% confident that the true proportion of judges who are introverts falls within this interval.

c)We are 1% confident that the true proportion of judges who are introverts falls above this interval.

d)We are 99% confident that the true proportion of judges who are introverts falls outside this interval.

(c) Do you think the conditionsnp>5 andnq>5 are satisfied in this problem? Explain why this would be an important consideration.

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

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

c)Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

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