Medical billing errors and fraud are on the rise According t

Medical billing errors and fraud are on the rise. According to Medical Billing Advocates of America, 8 our of 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:

a. 0 medical bills will contain errors?

b. exactly 5 medical bills will contain errors?

c. more than 5 medical bills will contain errors?

d. what are the mean and standard deviation of the probability distribution?

**Please show work, so I may understand how you solved it for future references** Thank you, so much!

Solution

PROBABILITY OF MEDICAL BILL CONTAINING ERROR = 8/10 = 0.8

PROBABILITY BILL NOT CONATINING ERROR = 1 - 0.8 = 0.2

A) 0 MEDICAL BILL CONTAIN ERROR = ALL BILL ARE REAL

10C0*(0.8)^0*(0.2)^10 = 0.00000001

B) 5 BILL VAONTAIN ERROR = 10C5*(0.8)^5*(0.2)^5 = 0.026

C) MORE THAN 5 CONATIN ERROR = P(6)+P(7)+P(8)+P(9)+P(10)

= 10C6(0.8)^6*(0.2)^4 +10C7*(0.8)^7*(0.3)^3 + 10C8*(0.8)^8*(0.2)^2 + 10C9*(0.8)^9*(0.2) + 10C10*(0.8)^10*(0,2)^0 = 0.088 + 0.201 + 0.301 + 0.268 + 0.107 = 0.956

D) MEAN IS SUM OF PROBABILITY / TOTAL CASES = 1/10 = 0.1

AND THE USING THE STANDARD DEVIATION FORMULA WE WILL GET IT BE EQUAL TO 2.356