# Help with some Learning Exercises

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• #51893

learning
Participant

Hello:
I am currently reading the book Implementing Six Sigma: Smarter Solutions Using Statistical Methods and have made it to Chapter 7…
There are a few exercises I am struggling with and thought perhaps someone could lend a hand. This is for a training class so I want to understand the answers…
3. The diameter of a shaft has µ = 75mm with a standard deviation of ợ = 8mm. Determine the proportion of the population of bushings that has a diameter of less than 65 mm.

4. Determine the proportion of the population described in the previous exercise that has a diameter between 55 mm and 95 mm.

5. An electronic manufacturer observed a mean of 0.20 defects per board. Assuming a Poisson distribution, determine the probability of three defects occurring on the same board.

20. A complete software system averages 7 errors per 5,000 lines of code. Determine the probability of exactly 2 errors in 5,000 lines of randomly selected lines of code. (Six Sigma Study Guide 2002.)

Any assistance is greatly appreciated.

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#181577

Hal
Participant

All questions are impossible to answer because in real world situations it is impossible to ever know the data distribution.
It takes 3200 measurements to determine the distribution to 2.95 sigma but by the time you do this, the distribution will have changed.
Tell your tutor the questions are meaningless.

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#181578

learning
Participant

Thanks for the quick response, but I believe there must be a way to answer these questions. They are contained in a training course so there must be some logical explaination. I have tried the following, but don’t know if this is correct.
Yet I am stuck on the additional questions…
3. The diameter of a shaft has µ = 75mm with a standard deviation of ợ = 8mm. Determine the proportion of the population of bushings that has a diameter of less than 65 mm.

Z = (65mm  75mm) / 8mm
Z = (-10 mm) / 8 mm
Z = -1.2
Table A yields P(x >= 65) = (P Z >= 1.2) = 0.1151 = 11.51% >=65)
Therefore 100% – 11.51% = 88.49% < 65 mm

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#181588

Gary Cone
Participant

Hal,Your input is meaningless. To paraphrase Montgomery – all models
are wrong, some models are useful.As someone who has been
doing this for over 30 years, understanding statistical models helps
you see the world differently. Working through problems such as
this helps change your thinking.To answer the questions – 3) This problem assume a normal distribution. It can be worked in
Excel using NormDist and the answer is 10.6%.4) Same assumptions, same excel function and the answer is
98.8%.5) Use the Poisson function in excel and the answer is 0.11%.20) Use the Poisson function in excel and the answer is 2.2%.If you need to be walked through this, contact me at
[email protected].

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#181606

BTDT
Participant

Gary:The attribution sounded familiar, so I did some digging and took out my copies of Montgomery. I found;First cited in a book chapter by George Box, “Robustness in the strategy of scientific model building, in Robustness in Statistics”, R.L. Launer and G.N. Wilkinson, Editors. 1979, Academic Press: New York.Then cited in “Empirical Model-Building and Response Surfaces” (Wiley Series in Probability and Statistics) 1987 by George E. P. Box, Norman R. Draper p. 424 “Essentially, all models are wrong, but some are useful.”By the way, stumbled across this site, http://curiouscat.net/library/georgebox.cfm,
It has copies of a number of interesting articles from Box including the original helicopter DOE design, and about “Quality Quandaries – Six Sigma, Process Drift, Capability Indices, and Feedback Adjustment”Cheers, Alastair

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#181608

Gary Cone
Participant

Alastair,
Thanks, I just looked and you are right. It was Box.