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November 13th, 2007, 10:45 PM  #1 
Newbie Joined: Nov 2007 Posts: 2 Thanks: 0  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? 
November 14th, 2007, 04:37 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
You could do it combinatorially. The chance that exactly n parts out of 400 are defective is .95^(400n) * .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(1p)) = sqrt(400 * 0.05 * 0.95). So use a ztable with those parameters. 
November 14th, 2007, 02:07 PM  #3 
Newbie Joined: Nov 2007 Posts: 2 Thanks: 0 
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 tscores and the like. I think I'm supposed to use some of that stuff.

November 14th, 2007, 06:17 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 

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