The only firm correlation between random error and uncertainty is that σ correlates with both the average absolute error and the root mean square error (RMSE). expect that errors sampled from σ < 5 are scaled by 1.25 making the set of errors 25% too high compared to the uncertainties, σ. Similarly the errors for σ > 5 are scaled with a factor or 0.8 making these errors 20% too low based on their uncertainties. (b) The |Z| distribution for σ < 5 no longer follows a normal distribution with a standard deviation 1. This half of the |Z|-distribution has a miscalibration area of 0.07. (c) Similarly the |Z|-distribution for σ > 5 no longer follows a normal distribution resulting in a miscalibration area of 0.07 (d) However, the total |Z|-distribution still follows a normal distribution quite well with a close to zero miscalibration area due to cancellation of error between the problematic behavior of the uncertainties for σ < 5 and σ > 5.