I have a problem I'm not sure how to solve. It goes something like:
Suppose we are manufacturing motherboards and we take a sample measuring their areas: [400, 400.1, 400.2, 399.99, 399.1, 400.3, 399.2, 399.99]. Give a 99% tolerance interval that will contain 95% of all manufactured cards (suppose it is a normal distribution).
From the information Provided:
n = 8 X (Sample mean) = 399.86 S (Sample STDEV) = 0.4525
Now, I know how to get 99% confidence interval for the mean using a small sample with the T distribution but I think that includes the whole population.
Question: How can I solve this problem?
I've found examples here and there but they are for Bernoulli distributions (success vs failure proportions).
The only relevant example I found is this, but I'm not sure how to use the given formulas to solve my problem.