Nowadays we deal with Big-Data commonly. The users of statistics rely on having a large sample size n for using the statistical methods based on normality. Usual inference methods are typically based on considering the Normal as the limit distributions of the sample mean for a large n. With large enough sample sizes (> 30 or 40), the violation of the normality assumption should not cause major problems. This fact implies that we can use parametric procedures even when the data are not normally distributed. Al least a goodness-of-fit test must be performed for accepting whether normality is valid or not. Monte Carlo (MC) techniques are used for selecting independent random samples of populations of means of three variables of importance in web network management. Different tests are performed to establish the acceptance of the normality. We did not find reliable results even for samples of size 10 000Nowadays we deal with Big-Data commonly. The users of statistics rely on having a large sample size n for using the statistical methods based on normality. Usual inference methods are typically based on considering the Normal as the limit distributions of the sample mean for a large n. With large enough sample sizes (> 30 or 40), the violation of the normality assumption should not cause major problems. This fact implies that we can use parametric procedures even when the data are not normally distributed. Al least a goodness-of-fit test must be performed for accepting whether normality is valid or not. Monte Carlo (MC) techniques are used for selecting independent random samples of populations of means of three variables of importance in web network management. Different tests are performed to establish the acceptance of the normality. We did not find reliable results even for samples of size 10 000