Our simulations generated 10 data points equally spaced between 0 and 20 minutes, adding Gaussian random error with a standard deviation of 10. The graph below shows three sample simulations. We simulated 5000 sets of data, and fit each data set to the exponential decay model expressed in three ways. At first glance, all three distributions look roughly Gaussian. Looking more carefully, you can see that the distribution of time constants is skewed to the right.
Careful scrutiny reveals that the rate constant distribution is also a bit skewed.
These impressions can be confirmed by a normality test. The results are shown in the following table. See The results of normality tests. None of the distributions are far from Gaussian. Because we simulated so many data sets, the KS test has the power to detect even modest deviations from a Gaussian distribution.