Problem 2 (25 points) Accepting or rejecting a shipment of CD systems. By mistak
ID: 3148750 • Letter: P
Question
Problem 2 (25 points) Accepting or rejecting a shipment of CD systems. By mistake, a manufacturer of CD mini rack systems includes 300 defective systems in a shipment of 1000 going out to a small retailer. The retailer has decided to accept the shipment of CD systems only if at most 2 units are found to be defective (such a nice retailer!). Upon receipt of the shipment, the retailer examines only 4 of the CD systems. (Hint: use the binomial distribution, for example probability of finding a defective CD is p 0.3, and it does not change as one extract CDs from the 1000-item shipment) a. (10 points) What is the probability that the shipment will be rejected? 5 the CD ylens. What s the psobab thad liprant l be accepted ith ongin ont C IV ageExplanation / Answer
This probablem is of binomial distribution with p = 0.3
a)
Probability that the shipment will be rejected
P(X>= 3) = 4C3*0.3^3*0.7 + 4C4*0.3^4
P(X>=3) = 0.0837
b)
Probability that the shipment will be accepted
P(X <= 2) = 5C0*0.3^0*0.7^5 + 5C11*0.3^1*0.7^4 + 5C2*0.3^2*0.7^3
P(X <= 2) = 0.83692
c)
Expected number of defective units
E(X) = np = 1000*0.3 = 300
d)
std. dev. = sqrt(1000*0.3*0.7) = 14.4914