A manufacturing company produces metal pipes with a desired width of 2.5 cm. Due to machine error, the pipes vary somewhat from this target. The company takes a sample of 100 pipes produced. The observed mean pipe width was approximately 2.502 and the sample standard deviation was 0.00932. The company also determined that the cutoff measurement for the widest 2.5% of pipes that were observed is 2.519. The research department of the company believes that the width of the pipes is normally distributed, with a mean of 2.5 cm and a standard deviation of 0.01. If that is the case, what should the cutoff be for the widest 2.5% of pipes be? Using any of the information above, do you think the research department’s beliefs about the distribution of the tube widths are plausible? Explain your reasoning. (Hint: How do the observed mean, standard deviation, and percentile cutoffs compare to the research’s teams baseline assumptions?) The box-and-whisker plot below represents the tube width data from the previous problem. One value is represented as a point. What is the significance of that? What does the line drawn through the blue box represent? What does the “x” inside of the box represent? What is the significance of the fact that the line and the “x” are in different places?

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

A manufacturing company produces metal pipes with a desired width of 2.5 cm. Due to machine error, the pipes vary somewhat from this target. The company takes a sample of 100 pipes produced. The observed mean pipe width was approximately 2.502 and the sample standard deviation was 0.00932. The company also determined that the cutoff measurement for the widest 2.5% of pipes that were observed is 2.519.

The research department of the company believes that the width of the pipes is normally distributed, with a mean of 2.5 cm and a standard deviation of 0.01. If that is the case, what should the cutoff be for the widest 2.5% of pipes be?

Using any of the information above, do you think the research department’s beliefs about the distribution of the tube widths are plausible? Explain your reasoning. (Hint: How do the observed mean, standard deviation, and percentile cutoffs compare to the research’s teams baseline assumptions?)

The box-and-whisker plot below represents the tube width data from the previous problem.

One value is represented as a point. What is the significance of that?
What does the line drawn through the blue box represent?
What does the “x” inside of the box represent?
What is the significance of the fact that the line and the “x” are in different places?

2.540
2.530
2.520
2.510
2.500
2.490
2.480
2.470
X

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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