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 of10,545convicts who escaped from certain prisons, only7441were 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 limit

upper limit

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

We are 1% confident that the true proportion of recaptured escaped convicts falls within this interval.

We are 99% confident that the true proportion of recaptured escaped convicts falls within this interval.

We are 1% confident that the true proportion of recaptured escaped convicts falls above this interval.

We are 99% confident that the true proportion of recaptured escaped convicts falls outside this interval.

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

Yes;np< 5 andnq< 5.

No;np< 5 andnq> 5.

No;np> 5 andnq< 5.

Yes;np> 5 andnq> 5.