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November 13th, 2007, 11:45 PM   #1
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need help with a statistics probability problem

I am looking at a sample of an infinite population of manufactured parts. The population is a normal distribution (whatever that means in this case, since I don't know the standard deviation) and 5% of the parts are known to be defective. Now my question:

5% of the manufactured parts of the infinite population are defective. Calculate the probability that the sample of 400 parts contains 36 or more defective parts.

How do I do this?
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November 14th, 2007, 05:37 AM   #2
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You could do it combinatorially. The chance that exactly n parts out of 400 are defective is .95^(400-n) * .05^n * (400 choose n), then sum this formula from 0 to 35 and subtract from 1. This is a use of the binomial formula, though it requires big numbers: 400 choose 35 is 24685184473786479717864752464078290163400663996640 0.

But you were asked to use the normal distribution, which is a great approximation for the binomial distribution at large numbers. The mean is easy to find, and the standard deviation for a binomial distribution is sqrt(np(1-p)) = sqrt(400 * 0.05 * 0.95). So use a z-table with those parameters.
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November 14th, 2007, 03:07 PM   #3
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You know, I think I posted this is the wrong section, because this is a college level statistics course and I have been dealing with sampling distributions of sample means and t-scores and the like. I think I'm supposed to use some of that stuff.
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November 14th, 2007, 07:17 PM   #4
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Quote:
Originally Posted by euromath
You know, I think I posted this is the wrong section, because this is a college level statistics course and I have been dealing with sampling distributions of sample means and t-scores and the like. I think I'm supposed to use some of that stuff.
Yeah, probably. Of course if it looked like a high school problem I probably wouldn't have answered it.
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