A recording company obtains the blank CDs used to produce its labels from three
ID: 2901576 • Letter: A
Question
A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 7% of the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II are defective, and 4% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 37%, 45%, and 18%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?
A. 0.0259
B. 0.0072
C. 0.0556
D. 0.0225
E. 0.1600
Explanation / Answer
Note that, as a multiple choice problem, you may solve this without doing any calculations, as the defectives in the 3 plants range from 4% to 7%, so any weightings of these 3 plants will be in this range, so the answer is C
The problem is actually worked out as .07*.37 + .05*.45 + .04*.18 = .0556 which is, of course, answer C.