Question: The width of a casing for a door is normally distrib- uted with a mean of 24 inches and a standard deviation of 1/8 inch.

The width of a casing for a door is normally distrib- uted with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23-7/8 inches and a standard deviation of 1/16 inch. Assume independence.

(a) Determine the mean and standard deviation of the differ- ence between the width of the casing and the width of the door.

(b) What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch?

(c) What is the probability that the door does not fit in the casing?

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