Normal statistics or not?

While, in general, metals and ceramics give reasonably consistent results, when working with mechanical properties of polymers and bonding agents it is not unusual to observe standard deviations of 50% of the group average or more. This should make any selection of statistical treatment debatable. For example, if the mean and standard deviation for a tested group of specimens is 10 ± 5, as shown in Figure 1 on the Gaussian distribution curve, 2.28% of the area under the curve is associated with data values less than zero. In most experimental situations it is physically impossible to have such values. Figure 2 shows a graph of the percentage of the Gaussian or normal curve having data values less than zero plotted versus the percentage of the standard deviation as related to the mean (i.e., 100 SD/mean), which is also known as the coefficient of variation. Examination of Figure 2 shows that at 100%, when the standard deviation equals the mean, then 15.87% of the normal curve is associated with values less than zero. Since the underlying assumption of statistics such as t and ANOVA is the normal distribution, how far away from that situation can anyone be and still satisfy the assumption? Judging from the shape of Figure 2, as a 'rule of thumb,' when the standard deviation is greater than 45% of the mean, one should consider utilizing other statistical distributions, such as Weibull and Logit, which do not generate data values less than zero.