For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of588potsherds was found, of which363were identified as Santa Fe black-on-white.

(a) Letprepresent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval forp. (Round your answers to three decimal places.)

Lower Limit: _____

Upper Limit: _____

Give a brief statement of the meaning of the confidence interval.

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