Value stream mapping - numbers needed

I was just asked for a power-calculation for a Value stream mapping proposal. Very odd. However, it got me thinking. If, as in this case, we are looking at time spent with a patient by different medical staff in an emergency department, how do we know if the few cases we follow are truly representative? We can, of course, for each component of the patient journey give measures of how the time varies. We could pick one component & do a power calc, but I think that is arbitrary and largely meaningless. Nevertheless, the point of the exercise is to understand what is typically happening in the ED and I can see some value in trying to work out how many cases we need to follow to understand the “typical” case. Any ideas?