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.
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.
The Assignment: (3–5 pages)
- 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?
- 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%.
- 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?
- 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%?
Expert Solution Preview
Introduction:
In this case, we are presented with the task of conducting a Medicare audit on Sleaze Hospital, which has a history of overbilling. Our objective is to determine if the billing amounts from the hospital are correct by using various probability strategies. In this assignment, we will answer the series of questions provided, which includes calculating probabilities for different scenarios.
1. 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?
To calculate the probability of finding at least 15 invoices that overcharge the customer, we can use the binomial distribution formula. Let X be the number of overcharged invoices. Then X has a binomial distribution with n=200, p=0.06, and q=0.94 (probability of a correct billing is 0.93, so the probability of undercharging is 0.01, or q=1-p).
P(X≥15) = 1 – P(X
