Advanced Placement (AP), 13.01.2021 17:20 annamcveigh50

The diameter C of the top of a randomly selected large drink cup at a fast-food restaurant follows a Normal distribution with a mean of 3.96 inches and a standard deviation of 0.01 inch. The diameter L of a randomly selected large lid at this restaurant follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inch. Assume that L and C are independent random variables. Let the random variable D=L−C be the difference between the lid’s diameter and the cup’s diameter. Describe the distribution of D.
For a lid to fit on a cup, the value of L has to be bigger than the value of C, but not by more than 0.06 inch. Find the probability that a randomly selected lid will fit on a randomly selected cup. Interpret this value.

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