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

Case studies showed that out of10,188convicts who escaped from certain prisons, only8287were recaptured.

(a) Letprepresent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval forp. (Round your answers to three decimal places.)lower limitupper limit

Give a brief statement of the meaning of the confidence interval.Chose 1

99% of all confidence intervals would include the true proportion of recaptured escaped convicts.

1% of all confidence intervals would include the true proportion of recaptured escaped convicts.

1% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

(c) Is use of the normal approximation to the binomial justified in this problem? Explain.

No;np> 5 andnq< 5.

Yes;np> 5 andnq> 5.

No;np< 5 andnq> 5.

Yes;np< 5 andnq< 5.