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
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
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?
Expert Solution
steps

Step by step

Solved in 3 steps with 7 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman