Answered: A particular manufacturing design…

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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A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.990 mm and 21.010 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.005 mm and a standard deviation of 0.006 mm.

Complete parts (a) through (d) below.

a. For this process, what is the proportion of shafts with a diameter between 20.990mm and 21.000 mm?

The proportion of shafts with diameter between 20.990 mm and 21.000 mm is .

(Round to four decimal places as needed.)

b. For this process, what is the probability that a shaft is acceptable?

The probability that a shaft is acceptable is .

(Round to four decimal places as needed.)

c. For this process, what is the diameter that will be exceeded by only 2.5% of the shafts?

The diameter that will be exceeded by only 2.5% of the shafts is 17.0118 mm.

(Round to four decimal places as needed.)

d. What would be your answers to parts (a) through (c) if the standard deviation of the shaft diameters were 0.006 mm? If the standard deviation is 0.006mm, the proportion of shafts with diameter between 20.990 mm and 21.000 mm is

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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