Question

1. Lexus Inc., has found that for the autos produced in the twelve month period from January 2017 through December 2017 of the 34000 LS 500's manufactured there was an average of 2 errors per car. What is the probability of an LS 500 built in this period having 0 errors? What is the probability of an LS 500 built in this period having 1 error? More than 2 errors? What is the mean and variance of the probability distribution? You can use the Excel sheet or Table from Sakai to calculate the results. 2. Medical billing errors and fraud are common in the U.S. Research by a major accounting firm found that 6 out of 20 medical bills contain errors. If a sample of 10 medical bills is selected, what is the probability that O medical bills will contain errors? Exactly 3 medical bills will contain errors? Exactly 6 medical bills will contain errors? More than 4 bills will contain errors? What is the mean and variance of the probability distribution? You can use the Excel sheet or Table from Sakai to calculate the results.

Answer 1

Poisson and Binomial distribution

1. Let x be the number of errors per car. Given that, an Poisson (2) So, required probabilities will come from the pmf of a. We know that, pmf of x is given by: P(x=x) = e-2, (2) / So, P(x=0)=0-2. (2)%, = 0.1353 P(x=1)=-(2), = 0.2707 P (x> 2) = 1- P(x2). = 1- P(x=0) - P(x=1) - P(x-2) Now, P(X=2) - e-?. (2), = 0.2707 :P(x>2) - 1-0'1353 -0.2707 -0.2707 = 0.3233 Foro poisson distribution, we know that mean - variance = 2.

2. Let x be the random variable that a bill contains empor, Given that, xn binomial (10,6/20). .. Pmf of x is given by : 14 10- P(x= x) = (10) Coli to 1. P(X=0) = (40) (09°C 1%) 40 -0.0282 P(X33) - (40) () *) * = 0.2668 PCX=6) = (10) 060) °C **)* = 0.0368

P(X34) = 1-PCX<4) al- (x=0) - P(x-1)-P(x=2) - P(x=3) - 1-0.6496 - 0:3504 .

Mean = 10 x 6 = 3 Variance = 10x6 x 14 = 2'1 , 20