Help with Sampling, Prediction Intervals, and T-distribution

[Remobeater]

Hello,

I'm just trying to remember some concepts from various statistics courses I took in college. This seems like a basic problem but I'm not getting a straightforward idea of how this works:

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I take a sample of 10 widgets and measure 10 values. I get a sample mean and sample variance. Now I would like to make a prediction based on these sample statistics what the distribution should be for 100 widgets, which have a normal distribution. I would like to know what the minimum value should be with 99.7% confidence (approximately 3σ from mean).
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It sounds like I should be able to use the t-distribution for this problem. I was looking through wikipedia and I found this formula for predicting distributions with unknown mean and variance:

Xn is the sample mean, Ta is the t value at a confidence level, with nd degrees of freedom, sn is the sample variance, and n is the number of samples.

Is this the proper way to do this estimation, or should I be using an estimation of population mean and standard deviation based on my sample?

Thanks,
Ian