Normal distribution and heavy tailed distribution are very important in probability theories. They have totally different mathematical forms and physical meanings. The probability density function of normal distribution decay exponentially to 0. The majority of normal random variable values are around the mathematical expectation. The tailed distribution function of the random variables that obey heavy tailed distribution shows heavy tailed characteristic. The probability density function decays power exponentially to 0.In this paper, we proved that the normal cloud model is heavy tailed distribution and its mathematical expectation exists.It is intermediate between notmal distribution and heavy tailed distribution. The parameter He(hyper entropy) of the normal cloud model is the bridge from normal distribution to heavy tailed distribution.