Confidence interval for an arbitrary distribution

[zeroes00]

Let's say we have a population of real numbers that are between -10 and 30. The values in the population most likely are not normally distributed but can be in any kind of distribution. The size of the population is infinite. Then we take 5 random samples from this population which are: -1.5, 3.3, 7.7, 12.3, 23.4. Now we'd like to estimate the mean of the population and the confidence interval of that estimated mean (using only these 5 samples and the knowledge that the values in the distribution are between -10 and 30). How would you go about doing this?

EDIT: I forgot to say that let's say we want to use 95% confidence level

 

[royhaas]

The sample mean will estimate the population mean. Without further information, it isn't realistic to construct a confidence interval because of the small sample size.

 

[zeroes00]

Okay, let's forget about confidence interval. Basically I'm trying to estimate the mean of a population by taking samples one by one. It takes long time for the computer to retrieve (simulate) a sample value, so I'd rather stop doing it as soon as I've got enough samples to calculate a reasonably accurate estimation of the mean. I figured the size of the confidence interval would be a good indicator of how certain I am that the sample mean is "close to being correct". But let's change the question to: "what kind of a method would you use for determining when you have retrieved enough samples to believe the sample mean is quite close to the population mean when we know the bounds of the population but not the distribution."