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Received a question from a reader this morning that will make a nice tutorial.
A box contains 27 black and 3 red balls. A random sample of 5 balls is drawn without replacement. What is the probability that the sample contains one red ball?
So here’s my thinking and two ways to solve this problem. Instead of red and black balls in an urn type problem, which is pretty abstract, let’s say we know 3 bad parts are in a bin of 30 total parts.
The operating characteristic curve is used to understand lot sampling plan. It graphically provides a relationship between the unknown lot’s defect rate (or total) and the probability of the specific sampling plan to accept the lot. Very good plans discriminate between good and bad lots. Poor plans may accept bad lots or reject good lots to easily. [Read more…]
In those situations where we sample without replacement, meaning the odds change after each sample is drawn, we can use the hypergeometric distribution for modeling. Great, sounds like statistician talk. So, let’s consider a real situation. [Read more…]