# Random Sampling around a Random Sample

Imagine I want to randomly sample how fast a driver is going on a highway. And for this purpose, let's assume that the distribution is normal with the mean as the speed limit. Now if I take a sample, that would give me a single speed that a driver might be going. But what I'd like to do is repeatedly sample how fast one specific driver is going. My thought process is to first sample on the previously mentioned distribution to get that specific driver's average speed, u1. Then perform many samplings on the new normal distribution with mean=u1.