sampling from confidence intervals If we are provided a mean and (95%) confidence interval, is it possible to set up a system in which we draw random values that are outside the CIs 5% of the time? 
My intuition is that if one can generate a distribution in which 68% of the random draws fall within a given interval, then it should also be possible to generate a distribution in which 95% of the draws fall within an interval.
Examples in R always helpful!
 A: Sampling from any distribution that has $\alpha_1$ of its probability below he lower limit of the CI and $0.05-\alpha_1$ of its probability above the upper limit of the CI (where $0\leq\alpha_1\leq 0.05$) should have the property you ask for.
So, you could choose a uniform distribution, or a normal distribution, or a t-distribution, or a Cauchy distribution - or almost anything else - as long as you chose the parameters so it had 2.5% of its probability below the lower limit and 2.5% of its probability above the upper limit. Sampling from that distribution will have 5% of its values outside the range.
e.g. Here's a 95% CI for the mean of a set of data: $(2893.238, 3061.930)$
So I could choose a uniform distribution, say. 
If 90% of its probability is inside that range (of width 168.692), then the full range of the uniform is 168.692/0.9 = 187.436 wide. 2.5% of that is 4.686, so I need a uniform that runs from 2893.236-4.686 to 3061.930+4.686.
5% of the values from that uniform will lie outside the CI.
