The least squares fit failed primarily because it favored the majority at the expense of a minority. The histogram cells closer to the mean time had the highest probabilities while those beyond the value of b had zero probability. The result was that the data for the last cell on the right could be ignored when computing the rms error of a trapazoidal distribution if the b value was too small.
The additional constraint for the minimum maximum magnitude of the z-scores for the probability distribution assured that an unlikely situation would not occur. The probability of a histogram interval was found by using the difference of the integral of the trapazoidal distribution of its upper and lower bounds.
When setting bounds for curve fits one has to make certain that significant data is not ignored.
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