# Estimating location of lower tail

#### EdddieB1985

##### New Member
Say I have a sample, assumed from a Normal Distribution. I want to find a confidence interval for this parameter:

$$L = \mu - \alpha * \sigma$$

where $$\alpha$$ is a known constant.

I guess I should use the estimator:

$$\bar{x} - \alpha*s$$

But what standard error should I use?

Just for context - the situation is that I have measured the size of 8 manufactured objects, and want to figure out a reasonable value for the minimum size that they might ever take.

Cheers! This is my first post, so I hope it makes sense, and the maths typesetting works.

#### rogojel

##### TS Contributor
hi,
this would be a nice occasion to use the bootstrap method. Just generate a bunch ( >100000)samples with replacement from your data and create the distribution of your value.

regards