University Assignment: Statistical Analysis of Medicare Overbilling

This assignment analyzes Medicare overbilling using statistical methods. It begins by defining variables for overcharged and undercharged invoices and calculates probabilities using the binomial distribution. The solution determines the probability of at least a certain number of invoices being overcharged and the probability of no undercharges. The assignment then uses the normal distribution to determine the probability that the percentage of overbilled invoices exceeds a certain threshold. The calculations include determining the mean, variance, and standard deviation of overcharged amounts. Finally, the assignment explores the probability of overbilling percentages and the probability of a minimum number of invoices exceeding a certain percentage using the normal distribution, providing a detailed statistical analysis of the Medicare overbilling scenario.

Running Head: MEDICARE OVERBILLING
Medicare Overbilling
Name of the Student
Name of the University
Author Note

1MEDICARE OVERBILLING
Answer 1
Let X be the number of invoices that are overcharged.
Let Y be the number of invoices that are undercharged
Sample size (n) = 200
Probability of being overcharged = 0.06
Probability of being undercharged = 0.01
Thus, we can say that X ~ Bin (200, 0.06) and Y ~ Bin (200, 0.01)
Therefore,
P (X ≥ 15) = 1 – P (X < 15) = 1 – P (X ≤ 14) = 1 – BINOMDIST (14, 200, 0.06, TRUE) = 1 –
0.778 = 0.222
The probabilities are obtained from Excel.
Thus, the probability that at least 15 invoices are overcharged is 0.222
The probability that there will be no undercharge to the customer is given by the following
probability:
P (Y = 0) = BINOMDIST (0, 200, 0.01, FALSE) = 0.134

2MEDICARE OVERBILLING
Answer 2
Using BINOMDIST function in Excel, it has been observed that for k = 20, the
probability will be at least 0.99. Thus, the probability will be at least 0.99 that there will be at
least 20 invoices that overcharge the customer.

3MEDICARE OVERBILLING
Answer 3
Let the distribution of amount overcharged be a normal distribution.
Let S be the overcharged amount
Mean (μ) = 15
Standard Deviation (σ) = 4
Probability that the percentage of overbilled invoices is at least 10% more than the legal billing
amount is given by
P (S > 10) = 1 – P (S < 10) = 1 – NORMDIST (10, 15, 4, TRUE) = 1 – 1056 = 0.8944
Thus, percentage of being overcharged = 89.44 %

4MEDICARE OVERBILLING
Answer 4
Sample size (n) = 200
The probability of being overcharged (p) = 0.06.
The mean of being overcharged = (n * p) = (200 * 0.06) = 12
The variance of being overcharged = n * p * (1 – p) = 200 * 0.06 * 0.94 = 11.28
The standard deviation of being overcharged = √np(1− p) = 3.36
Probability that the percentage of all invoices is at least 10% more than the legal billing amount
is given by
P (S > 10) = 1 – P (S < 10) = 1 – NORMDIST (10, 12, 3.36, TRUE) = 1 – 0.2758 = 0.7242
Thus, percentage of being overcharged = 72.42 %

5MEDICARE OVERBILLING
Answer 5
Sample size (n) = 200
The probability of being overcharged (p) = 0.06.
The mean of being overcharged = (n * p) = (200 * 0.06) = 12
The variance of being overcharged = n * p * (1 – p) = 200 * 0.06 * 0.94 = 11.28
The standard deviation of being overcharged = √np(1− p) = 3.36
Probability that at least 5 all invoices is at least 10% more than the legal billing amount is given
by:
P (S > 5) = 1 – P (S < 5) = 1 – NORMDIST (5, 12, 3.36, TRUE) = 1 – 0.0186 = 0.9814