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# The width of a casing for a door is normally distributed

ISBN: 9781118539712 55

## Solution for problem 68E Chapter 5.4

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 68E

The width of a casing for a door is normally distributed 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 difference 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 fi t in the casing?

Step-by-Step Solution:
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Statistics: Chapter 3.1 1. Mean: average of a set of numbers a. (sum of all data values) / (number of values) b. Mean = (Σx) / (n) i. Let x be a quantitative variable with n measured data value from a population of n. c. Example: i. 10, 15, 20, 25….625 ii. (n+1) / 2 iii. “n”...

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