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this is the problem:

we wish to estimate the mean execution time of a program. the program was run 35 times on randomly selected inputs, and the sample mean and the sample standard deviation of the execution times were evaluated as (x bar)=230ms, and S(sample sd)=14ms, respectively. find 95% CI for the true mean execution time u

what and how can you tell this is a non-normal population. i knew it because it is an example under "Large sample CI for non-normal population"

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Almost nothing is normal. The distribution of long enough sums (and therefore averages) of independent identically distributed "nice" random variables are well approximated by a normal. – André Nicolas Dec 10 '12 at 18:21

There is not enough information here to tell that it's not normal. The point is that because the sample size is somewhat large, it doesn't matter that it's not normal, because of the central limit theorem. However, the sample is not so large that I wouldn't use Student's t-distribution. You'd have $34$ degrees of freedom.

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