The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean 28.4 and standard deviation 2.95 (in appropriate units). To ensure safety, a customer requires at least 95% of the bars to be stronger than 24.0. a.) Do the bars meet specifications? (That is, are there at least 95% of bars exceeding 24.0²) b.) By improved manufacturing techniques the manufacturer can make the bars more uniform (that is, decrease the standard deviation). What value of the standard deviation will just meet the customer's specification if the mean stays the same?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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The strengths of individual bars made by a certain
manufacturing process are approximately normally
distributed with mean 28.4 and standard deviation 2.95
(in appropriate units). To ensure safety, a customer
requires at least 95% of the bars to be stronger than
24.0.
a.) Do the bars meet specifications? (That is, are there
at least 95% of bars exceeding 24.0?)
b.) By improved manufacturing techniques the
manufacturer can make the bars more uniform
(that is, decrease the standard deviation). What
value of the standard deviation will just meet the
customer's specification if the mean stays the
same?
Transcribed Image Text:The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean 28.4 and standard deviation 2.95 (in appropriate units). To ensure safety, a customer requires at least 95% of the bars to be stronger than 24.0. a.) Do the bars meet specifications? (That is, are there at least 95% of bars exceeding 24.0?) b.) By improved manufacturing techniques the manufacturer can make the bars more uniform (that is, decrease the standard deviation). What value of the standard deviation will just meet the customer's specification if the mean stays the same?
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