PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test. In addition, many in-process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades during the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Drawing upon your experience, you have developed a number of questions:For the mower test data, what distribution might be appropriate to model the failure of an individual mower?What fraction of mowers fails the functional performance test using all the mower test data?What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20?What is the average blade weight and how much variability is occurring in the measurements of blade weights?Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?What is the probability that weights will be less than 4.80?What is the actual percentage of weights that exceed 5.20 or are less than 4.80, from the data in the worksheet?Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of the blade weights?Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process or materials?Was the assumption that blade weights are normally distributed justified? What is the best-fitting probability distribution for the data?

Solution: 1) The mower test date consists of only theresponses Pass or Fail. Since, there are…

Answered: studies, many of which are related to…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test. In addition, many in-process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades during the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Drawing upon your experience, you have developed a number of questions:

For the mower test data, what distribution might be appropriate to model the failure of an individual mower?
What fraction of mowers fails the functional performance test using all the mower test data?
What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20?
What is the average blade weight and how much variability is occurring in the measurements of blade weights?
Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?
What is the probability that weights will be less than 4.80?
What is the actual percentage of weights that exceed 5.20 or are less than 4.80, from the data in the worksheet?
Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of the blade weights?
Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process or materials?

Was the assumption that blade weights are normally distributed justified? What is the best-fitting probability distribution for the data?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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