5.3.28. University officials are planning to audit 1586 new appointments to estimate the proportion p who have been incorrectly processed by the payroll department. (a) How large does the sample size need to be in order for X, the sample proportion, to have an 85% chance of lying within 0.03 of p? n (b) Past audits suggest that p will not be larger than 0.10. Using that information, recalculate the sample size asked for in part (a).

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