the area under a standard normal density curve with mean of 0 and standard deviation of 1 is
The Normal Distribution. The Standard Normal curve, shown here, has mean 0 and standard deviation 1. If a dataset follows a normal distribution, then about 68% of the observations will fall within of the mean, which in this case is with the interval (-1,1).bout 95% of the observations will fall within 2 standard deviations of the mean, which is the interval (-2,2) for the standard normal, and about 99.7% of the observations will fall within 3 standard deviations of the mean, which corresponds to the interval (-3,3) in this case.