Question: Packaging CDs (6.2, 5.3) A manufacturer of compact discs (CDs) wants to be sure that their CDs will fit inside the plastic cases they have bought for packaging. Both the CDs and the cases are circular. According to the supplier, the plastic cases vary Normally with mean diameter μ = 4.2 inches and standard deviation σ = 0.05 inches. The CD manufacturer decides to produce CDs with mean diameter m = 4 inches. Their diameters follow a Normal distribution with σ = 0.1 inches.
(a) Let X = the diameter of a randomly selected CD and Y = the diameter of a randomly selected case.
Describe the shape, center, and spread of the distribution of the random variable X - Y. What is the importance of this random variable to the CD manufacturer?
(b) Compute the probability that a randomly selected CD will fit inside a randomly selected case.
(c) The production process actually runs in batches of 100 CDs. If each of these CDs is paired with a randomly chosen plastic case, find the probability that all the CDs fit in their cases.