Determining confidence interval from non-negative sample mean and standard deviation

I have a situation where I am receiving a set of values, which cannot be negative. From a given sample, I need to estimate the sample value threshold above which a percentage of the samples will reside.

As the sample mean moves away from zero, say towards 100, the standard deviation tends to decrease and the distribution appears to "match"/"resemble" the normal distribution. However, as the sample mean reduces, say to 15 or 20, the standard deviation tends to be higher. At this level the sample values seem to arise in "waves" of lower values and then rising to higher values and then back to lower values - similar to stop start motorway traffic in congestion. However, very few values are very close to zero (e.g. 1).

What formula may I apply to convert a sample's mean and standard deviation into the estimated value above which X% (e.g. 70% or 85% or 95%) of the next sampled values will be? I know I cannot just subtract one standard deviation from the mean for 70% or two standard deviations for 95%, because in samples with a low mean, the result returned can be less than zero, despite this not being possible due to the non-negative constraint. Even a zero value is not possible.

Thanks for any help you can provide.