example Question for estimating sample size

The state education commission wants to estimate the fraction of tenth-grade students that have reading skills at or below the eight grade level. In an earlier study, the population proportion was estimated to be 0.16.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Your company is running a Medicare audit on Sleaze Hospital. Because Sleaze has a history of overbilling, the focus of your audit is on checking whether the billing amounts are correct. Assume that each invoice is for too high an amount with probability 0.06 and for too low an amount with probability 0.01 (so that the probability of a correct billing is 0.93). Also, assume that the outcome for any invoice is probabilistically independent of the outcomes for other invoices.

probability Question using Excel

1. For this Assignment, reflect on the case presented. Think about what
   strategies you might use to calculate associated probabilities for
   Sleaze Hospital, and then address the series of questions for the
   completion of the Assignment.
2. If you randomly sample 200 of Sleaze's invoices, what is the
   probability that you will find at least 15 invoices that overcharge
   the customer? What is the probability you won't find any that
   undercharge the customer?
3. Find an integer, k, such that the probability is at least 0.99 that
   you will find at least k invoices that overcharge the customer.
   (Hint: Use trial and error with the BINOMDIST function to find k.)
   Suppose that when Sleaze overcharges Medicare, the distribution of
   the amount overcharged (expressed as a percentage of the correct
   billing amount) is normally distributed with mean 15% and standard
   deviation 4%.
4. What percentage of overbilled invoices are at least 10% more than
   the legal billing amount? What percentage of all invoices are at
   least 10% more than the legal billing amount?
5. If your auditing company samples 200 randomly chosen invoices, what
   is the probability that it will find at least five where Medicare
   was overcharged by at least 10%?
6. Submit your answers and embedded Excel analysis as a Microsoft Word
   management report.