Medical billing errors and fraud are on the rise. According to the MBAA website

Question

Medical billing errors and fraud are on the rise. According to the MBAA website 8 to 10 times, the medical bills that you get are not right. If a sample of 10 medical bills is selected what is the probability that more than 5 medical bills will contain errors? Medical billing errors and fraud are on the rise. According to the MBAA website 8 to 10 times, the medical bills that you get are not right. If a sample of 10 medical bills is selected what is the probability that more than 5 medical bills will contain errors?

Explanation / Answer

Here we can use the binomial distribution because the following requires four assumptions are satisfied:

1) sample size (n) is fixed here n = 10 so this assumption satisfy

2)Each replication of the process results in one of two possible outcomes success and failure (Fraud or not fraud),

3)The probability of success (probability of fraud) is the same that is constant for each replication, and

Here According to the MBAA website 8 to 10 times, the medical bills that you get are not right so p= 8/10 = 0.8 is same and hence constant.

4) The replications(that is trials) are independent,

here the success in one medical bill does not influence the probability of success in another medical bill .

So all the assumption are valid and we can use Binomial distribution to find the probabilities.

Here we want to find

the probability that more than 5 medical bills will contain errors.

that is P(X > 5) = 1 - P(X < = 5)

By using excel we get P(X < = 5) = 0.032792

The excel command is =BINOMDIST(5,10,0.8,1)

5 = number of success , n = 10 = total number of trials = sample size

p= probability of success = .8

here we find less than or equal probability so cumulative = 1

P(X > 5) = 1 - P(X < = 5) = 1 - 0 .32793 = 0.967207

So the probability that more than 5 medical bills will contain errors is 0.967207

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