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A manufacturer of CD's wants to be sure that their CD's will fit inside the plastic cases they have purchased to hold them. Both CD's and CD cases...

A manufacturer of CD's wants to be sure that their CD's will fit inside the plastic cases they have purchased to hold them. Both CD's and CD cases are circular. According to the supplier, the plastic cases vary normally with mean diameter of 4.2 inches and standard deviation of 0.05 inches. The CD manufacturer decides to produce CD's with mean diameter of 4 inches, and a normal distribution with a standard deviation of .1 inches.

a) Let X be 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 significance 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 runs in batched of 100 cd's. IF each of these 100 CD's is randomly paired with a case, find the probability that all the CD's will fit in the cases.

d) Manufacturers are concerned that too many CD's will not fit the cases, thereby slowing down the production process. Design a simulation using Table B to determine how many CDs in a typical production batch don't fit their cases. Describe your simulation carefully so that another classmate could obtain the same results. Carry out the simulation. What advice would you give the CD manufacturer?

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