Smart math people (statistics), step inside

[Ruffy]

My math is rusty and didn't pay attention in those two semesters in statistics I took in college, so...

A tolerance of 5% for a particular defect in a sample size of 100 is acceptable. I have assumed that the distribution of defects is normal. However, it can't be completely normal because there can't be less than zero defects in a sample.

How does this screw up the confidence interval? Regular CI is 99.7% @ ±3σ but that can't work because the µ is 1.25 and the σ is 0.97. You run out of room on the bottom end a little over 1σ.

I wish I didn't stop paying attention in math class after 8th grade...

[GRN ENVY]

You can have negative numbers on the left side of your mean. You would need to look at a Z-score number to find the tolerance of which would be acceptable

Negative Z Scores Chart, Normal Distribution Table (http://easycalculation.com/statistics/negative-z-score-chart.php)

[Sea Six]

[dab]I was told there would be no math.

[Ruffy]

You can have negative numbers on the left side of your mean. You would need to look at a Z-score number to find the tolerance of which would be acceptable

Negative Z Scores Chart, Normal Distribution Table (http://easycalculation.com/statistics/negative-z-score-chart.php)

I know I can have a number less than the mean but I can't have less than zero defects which means its like a bell curve with a good amount of the left side of the curve cut out. Or maybe I just don't understand what you are telling me

[C5SilverBullet]

13


:leaving:

[jaxgator]

42! The correct answer is 42. :yesnod:

[ZipZap]

Defect curves are rarely a normal distribution as zero defects returns a positive probability. Is 2.5 the mean? What is your assumption for the probability of zero defects? Set that to the same probability of 5 defects and then the distribution will be normal, but truncated. You can then integrate the area under the curve to determine confidence.

[Ruffy]

Mean is 1.25. I don't have an assumption for zero defects other than using the mean and standard deviation to calculate it.

There is an inline defect-detector that is supposed to remove all of the defect. However, due to the nature of the process, more defects can be created before packaging is completed.

Ignoring the total number of...let's call them...widgets produced, how do I use what I have to calculate the percentage of samples that would exceed the 5% defect tolerance? So far, no samples have exceeded this level.

[Ruffy]

The answer was 2-fold.

1)
The CLT states that the bigger a sample size gets, the closer to normal it becomes.

2)
http://upload.wikimedia.org/math/9/8/a/98a550e5fc94e32d527528ccb45da54b.png

[NeedSpeed]

What are you trying to determine?

[Milton Fox]

I like pi :cheers:

[Czarvette]

My math is rusty and didn't pay attention in those two semesters in statistics I took in college, so...

A tolerance of 5% for a particular defect in a sample size of 100 is acceptable. I have assumed that the distribution of defects is normal. However, it can't be completely normal because there can't be less than zero defects in a sample.

How does this screw up the confidence interval? Regular CI is 99.7% @ ±3σ but that can't work because the µ is 1.25 and the σ is 0.97. You run out of room on the bottom end a little over 1σ.

I wish I didn't stop paying attention in math class after 8th grade...

Try working with the Poisson distribution instead. As you discovered, the Gaussian approximation breaks down in your particular case.

[ZipZap]

You just put up the basic equation for the normal distribution function. How did this help you solve your question?

[Czarvette]

Oh, and just be crystal clear:

OP, is this the problem you're trying to solve?

"given a defect rate of 1.25% (probability that an individual widget is defective)what is the probabibility of 6 or more defective widgets in a lot of 100?"

If so, the exact probability will be given through application of the binomial probability function. The Poisson PDF approximates this well especially for edge cases. The Gaussian works where sample size is very large and mean is several SD away from the ends of range.

Gotta go finish mounting snowplow and chains on my tractor, be back later. :barnbabe:

[Czarvette]

Accidental dupe deleted

[Doug28450]

What are you trying to determine?

Which new TV to buy.

[snide]

What are you trying to determine?

Which new TV to buy.

Whether to eat the last slice of pie or not.

[onedef92]

http://i849.photobucket.com/albums/ab60/darine3007/2qt8ufm.gif

My head hurts...