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 of522judges, it was found that285were 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.

• 1. We are 1% confident that the true proportion of judges who are introverts falls above this interval.
• 2. We are 99% confident that the true proportion of judges who are introverts falls within this interval.
• 3. We are 1% confident that the true proportion of judges who are introverts falls within this interval.
• 4. 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.

• 1. Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.
• 2. No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.
• 3. Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.
• 4. No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.