An asymptotic distribution is a probability distribution that is the limiting distribution of a sequence of distributions. Since normal distributions are the limiting distribution for many other distributions and thus normal distributions are asymptotic. Normal distributions are considered to be a family of distributions, because you obtain a different normal distribution when you have a different mean and/or a different standard deviation. A normal distribution is also symmetric about its mean and thus 50% of the observations in a normal distribution are greater than the mean. The property that does not hold for a normal probability distribution is then "only two outcomes," which is true as a normal probability distribution has infinitely many possible outcomes. Result: Only two outcomes.