I have a few statistics problems that I don't have solutions for and am having trouble solving them. I'm hoping that someone can give me a boost as to which equations are appropriate, and more importantly, WHY you need that equation rather than a different one. I've tried solving these a couple of different ways and still can't hit the answer.

Problem 1:

What is the percent yield for a normally distributed process in which the item length specification is 5.750 +/- 0.005, Xbar is 5.745, and the standard deviation is 0.002.

Problem 2:

A process is running 1.5% defective. The sampling plan used for this process is n=40, accept/reject = 2/3. What is the probability of rejecting a lot from this process?

Problem 3:

If a distribution is normal, with u=50 and sigma=15, what percentage of data will be less than 30. This one I was able to get within a tenth of the real answer, but I think that might be luck...

Problem 4:

They give a table of 7 draws of five samples and ask for the UCL for the average. Another easy problem that I cannot get.

I don't think these problems are difficult, but for whatever reason, I'm just not getting them.

Any help you could provide would be great. I don't need the solution worked all the way out, I just need to understand the process and why to use that process rather than the others.

Why don't you tell us WHERE you are getting these problems?

Is this a primer for an upcoming certification exam? Boss beating you up to see how much you know? What?

Since you say,
"This one I was able to get within a tenth of the real answer, but I think that might be luck..."
It's obvious you have access to the answers (regardless whether they are right or wrong - you'd be surprised how many text books are plagued with errata.)

Wes, you are right - I should have posted the source of the problems. These are off the CQT sample exam that I pulled off the ASQ website. The sample does provide numerical answers, but no explanation of the solutions.

Should I not post these sorts of questions?

Moderator... please delete if this is inappropriate.

Holly -

I don't think Wes meant to be hostile. I believe it's OK to ask help, although I at least won't usually do the whole thing for anyone.


Problem 1:

What is the percent yield for a normally distributed process in which the item length specification is 5.750 +/- 0.005, Xbar is 5.745, and the standard deviation is 0.002.
Don't need to calculate anything. Look at the relationship of the sample mean, Xbar to the LCL. Technically there are some that are defective above the UCL, but they are in the hundredths of a %, so not meaningful.

Problem 2:

A process is running 1.5% defective. The sampling plan used for this process is n=40, accept/reject = 2/3. What is the probability of rejecting a lot from this process?
You are given the probability of a defect, the number in a sample, and the number you are interested in finding, the reject number 3. Use binomial distribution to figure probability of getting 3 or more in 40.
Why? Because it is discrete data and it is PASS/FAIL. Somewhere in your preparation materials, you should find something saying to use binomial in this case. Technically it is hypergeometric, but with this sample size, the binomial approximation will hold.


Problem 3:

If a distribution is normal, with u=50 and sigma=15, what percentage of data will be less than 30. This one I was able to get within a tenth of the real answer, but I think that might be luck...
You should be calculating the Z value for 30 within the distribution with u=50 and sigma = 15. If you did that and looked up the P(x<Z(30) in a table, you did it right. If you are only a little off, what precision did you use? Did you have to interpolate in the table?
That might explain it.

Problem 4:

They give a table of 7 draws of five samples and ask for the UCL for the average. Another easy problem that I cannot get.
You just need to construct a simple Xbar and range or xbar and s chart with 7 subgroups of 5. Find the UCL of xbar chart. Review your material on constructing these charts.

Good luck and please let me know if you need more hints, I can be too cryptic at times.

I'll look these over tonight. Thanks so much for taking the time! Statistics is really challenging for me, even though I've taken lots of higher level math for my engineering degree. I think I can do okay on the CQT, but to prepare for the CQE I think I'm definitely going to need some classes.

Thanks again!

I'm not hostile. I want to help. If we had known you were working for CQT stuff, we could have suggested lots of sources to help you understand what is going on in the exam. I, personally, have absolutely no familiarity with the CQT. Many of our Cove members hold the CQE designation. Most will tell you that the exams are structured so you have to answer each question in less than 90 seconds or so.

Often, local ASQ Sections provide low cost courses to help CQE candidates get all the tips and tricks to help them pass the exam. This is not an easy exam. None of the ASQ Certification exams are easy. Some years, the pass rate falls to about 50%, meaning 1/2 the people who take the exam fail. Almost always the reason for failure is related to a certain amount of hubris in feeling "I know how to do this" without sufficient practice on working the practice tests for time.

Knowing you were aiming at the CQT would have encouraged folks to suggest study guides which are more forthcoming with the "background and explanation of solution" of problems rather than just the answers.
Hostile? Nope. Just trying to get you to tell us the things that will help us help you.

I regretted the "hostile" line and went back and edited... I guess not soon enough! I apologize. I realized afterward that I may have misunderstood your tone and hadn't had my cup of coffee yet. :o

I've had a chance to look through some of the explanations that Dave posted and am still having trouble:

Problem 1:

There are no choices that indicate a very small percentage. The choices are 19.15%, 30.85%, 50.00%, and 69.15%. The correct answer is 69.15%.

Problem 2

When using the binomial formula with n=40, r=3 and p=.015 I arrive at .0190. The correct answer is.0221. I ran this twice and am pretty adept at using a calculator.

I haven't gotten to the other two yet. I'm pretty frustrated at this point with statistics. It's really the last thing I need to familiarize myself with before the test on March 5.

I've been trying to locate some sort of guide that summarizes the various conditions for each of the different types of formulas. I've also been making my own notes as I go along.

I have several reference books at the house, and even a couple different CQT/CQE refreshers. These all use the formulas, and present examples very similar to the ones you mentioned. I'm sure I waded thru these or similar when I took the CQT and the CQE.

They are really not hard to be honest. Also be advised that occasionally even the ASQ organization makes mistakes on exams, that are found later. You might have one of these BETA versions that don't list the "correct" answer. Also be advised that often these questions are SUBMITTED by ASQ members for credit. They assume that the problem is worked a certain way, using a certain formula protocol. If the question is investigated differently it will often yield a different answer.

I'm a little covered up today. When are you seated to take the exam?

Holly:

I don't know about the CQT, but the Quality Council of Indiana CQE primer sure helped me prepare. Also, I did not have a class nearby, but there were 3 of us working towards sitting for the exam at the time, and our study group was a very big help for me. Maybe you can find someone else near you who is also working towards the exam.

Holly:

I don't know about the CQT, but the Quality Council of Indiana CQE primer sure helped me prepare. Also, I did not have a class nearby, but there were 3 of us working towards sitting for the exam at the time, and our study group was a very big help for me. Maybe you can find someone else near you who is also working towards the exam.
That is a wonderful suggestion! Also try to find at least one local person who has taken the exam to act as a sounding board in addition to the sounding board offered here on the Cove.

I would first get in touch with a local ASQ Section head and ask for contacts, regardless of whether you are an ASQ member.

The exam is March 5.

Right now as references and resources, I'm using the CQI Primer, Solutions Manual, and test questions, the CQT Handbook, and Juran's Quality Control Handbook. At first, I was using the CQI for the stats, then realized that I needed something a bit more basic and have used a couple of different resources. I should go back to the Primer and see if it makes a little more sense now. The information presented there is much more concise than my other sources.

Passing first the CQT and then CQE are requirements of my job, which I started in November. Frankly, I was hired due to my engineering and manufacturing experience under the condition that I become versed in quality. For each test that I pass, I'll also receive a financial incentive to the tune of about 14% salary increase. I'm a little stressed out because my company has paid for all of my materials and exam fee, so I feel somewhat pressured to be sure I pass. (I'm pretty happy with my salary, so t's not just about the $$ either, that's just icing on the cake as far as I'm concerned). I'll be sitting for the CQE in December. Hopefully by then, some stats classes will be offered at the local college (right now they're into Stats II).

My local chapter does not offer any sort of review or refresher course, although the local community college has a Quality Certification Program where many members of my local chapter teach. That will be more of a resource for me for the CQE. For the is test, the timing didn't really mesh with the course schedule.

OK.. that's more than you wanted to know, I'm sure, but I'm new here. Everyone here has been really great about answering my questions.

Problem 1:

There are no choices that indicate a very small percentage. The choices are 19.15%, 30.85%, 50.00%, and 69.15%. The correct answer is 69.15%.

Problem 1:

What is the percent yield for a normally distributed process in which the item length specification is 5.750 +/- 0.005, Xbar is 5.745, and the standard deviation is 0.002.


OK, let's reason this out. The process is normally distributed with a mean of 5.745 and a standard deviation of 0.002. That means I can use normdist in excel to figure this out.

First, let's figure out the probability of exceeding 5.750 + .005, which is 5.755.

This is =1-NORMDIST(5.755,5.745,0.002,TRUE), which is a very very small number. Five standard deviations from the average.

Now, this is a two sided limit. So what is the probability of being below 5.750 - .005, which is 5.745? Seems to me, that is pretty straight forward - the probability of being below the mean is 50%. So, I would have said the answer is 50%.

If the book answer is 69%, working backwards that is basically 1/2 standard deviation from the average. There doesn't seem to be anything in the problem related to 1/2 standard deviation (unless this is some sort of six sigma-ish problem with the so-called 1.5 standard deviation shift).

Holly -

Your posting a couple of days ago said that for the first question did not have a very small value. I was too obtuse I guess. I was trying to lead you to the fact that the sample mean and the LCL were the same value, so 1/2 the parts are potentially defective. In such a case,there is a possibility that you can have some parts out of spec above the UCL but in this case the UCL is 5 sigma away, so the amount is not worth calculating if you are looking for a percentage. It is <<< 1%. So as Steve later showed, the 69% answer is wrong. 50% is the correct figure.

On problem two, whether I work it as binomial or use the Poisson approximation, I also get 0.0190 as the answer. Again the solution manual you have is wrong.

Is your material from Quality Council of Indiana? They are usually real good. Could you possible have the wrong answer sheet or have skipped a row or two? I blush to even suggest it. :o

How are you doing on the other questions?

Dave

I have written solutions for all of the QCI questions. These questions were from the CQT sample exam on the ASQ website. :-) They are questions 9 and 16.

http://www.asq.org/cert/pdf/cqt_sample_exam.pdf

I've double checked and it appears that for both of these problems, they have the wrong answer indicated. (Which certainly makes me feel better!) I haven't had a chance to work the other problems I listed yet. Thanks for all of your help.

One other thing that is confusing me.... is there a sure fire way to tell whether to use the binomial equation of the z table to calculate problem solutions? Some are obviously z table solutions (the problem states a normal distribution), however some problems I'll use the binomial, get the wrong answer, then look at the solution and they are using the z table...

Another question I have. Somewhere I read that the UCL and LCL were equivalent in most cases to 3sigma.... is there a special case where that is true?

Fortunately, before I take the CQE (or retake the CQT) at the end of the year, I should have the opportunity to enroll in a statistics course! I've never taken statistics before and am trying to figure all this stuff out on my own. My biggest problem is figuring out which formula to use.

I've tried creating an overview sheet listing the special cases when each one is used, gleaning information from three different sources, but even then, I'll think I'm using the right solution and find that it's the wrong formula... again. :frust: I've taken advanced math classes through partial differential equations and always got A's.... statistics, however, is a mystery to me. I've got a little less then 3 weeks to figure it out.

I have written solutions for all of the QCI questions. These questions were from the CQT sample exam on the ASQ website. :-) They are questions 9 and 16.

http://www.asq.org/cert/pdf/cqt_sample_exam.pdf

On Question 9, you copied the text over here incorrectly. The correct text is:

9. What is the percent yield for a normally distributed
process in which the item length specification is
5.750 ± 0.005, X bar is 5.754, and the standard deviation is
0.002 ?
(A) 19.15%
(B) 30.85%
(C) 50.00%
(D) 69.15%

That makes the upper specification limit at 5.755, and the xbar at 5.754, which would be 1/2 standard deviation away, which leads to the 69.15% answer. Note - the lower specification is 5.645, which is more than 4 standard deviations from the average.