Answered: The machine to produce metal wire has…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The machine to produce metal wire has been set so that the average length of the produced metal wire
is 300 cm with standard deviation of 5 cm.
A new regulation states that any produced metal wire
found to be shorter than 290 cm will be discarded.
To reduce the percentage of discarded products,
there are two suggestions for the adjustment of the machine:
Method I: Adjust the new mean to 303 cm and the standard deviation is unchanged, OR
Method II: The mean is unchanged and adjust the new standard deviation to 4 cm.
(a)
Calculate the percentage of discarded products if Method I adjustment is used.
(b)
Calculate the percentage of discarded products if Method II adjustment is used.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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