Answered: Ten percent of the fiber produced by…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

4. A fiber-spinning process currently produces a fiber whose strength is normally distributed with a
mean of 75 N/m2. The minimum acceptable strength is 65 N/m2 .
a. Ten percent of the fiber produced by the current method fails to meet the minimum
specification. What is the standard deviation of fiber strengths in the current process?
b. If the mean remains at 75 N/m2, what must the standard deviation be so that only 1% of the
fiber will fail to meet the specification?
c. If the standard deviation is 5 N/m2 , to what value must the mean be set so that only 1% of the
fiber will fail to meet the specification?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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