# Sample question

• Aug 26th 2006, 11:46 AM
andy_atw
Sample question
I have been away from math for a while. I appreciate the help here tremendously.

the problem: In manufacturing, a sample of 4 items from a lot of 100 is taken.
The lot is rejected if at least 1 is defective.
Graph the probability that the lot is accepted as a function of the percentage of defective items in the lot.

I included an attachment that tries to explain my thought process on the attached problem. I am completely stuck like chuck on the graph also.

If the attachment doesn't work I saved it to a link also.

Andy

• Aug 26th 2006, 01:29 PM
JakeD
Quote:

Originally Posted by andy_atw
the problem: In manufacturing, a sample of 4 items from a lot of 100 is taken.
The lot is rejected if at least 1 is defective.
Graph the probability that the lot is accepted as a function of the percentage of defective items in the lot.

A lot is accepted if none are defective. So the probability is $P(\text{accepted}) = P(4\ \text{not\ de{f}ective}) = (1 - k/100)^4 .$
• Aug 26th 2006, 04:07 PM
andy_atw
explain
Jake...I have been pondering the problem for a while now, and I am not grasping the logic in determining the answer. please explain further. thanks
• Aug 26th 2006, 06:29 PM
JakeD
Quote:

Originally Posted by andy_atw
Jake...I have been pondering the problem for a while now, and I am not grasping the logic in determining the answer. please explain further. thanks

Arghh, you're right. Sorry about that. I used a sample with replacement. This should be a sample without replacement.

So using the hypergeometric distribution the probability of no defectives is $\frac{{k \choose 0}{100-k \choose 4}}{{100 \choose 4}} = \frac{{100-k \choose 4}}{{100 \choose 4}}.$ This is the number of ways of choosing 4 out of 100-k nondefectives over the number of ways of choosing 4 out of 100.