Statistical Inference: A Short Course

6.2 The Normal Distribution

A continuous random variable has a normal distribution if its probability density function is bell-shaped, symmetrical about its mean , and asymptotic to the or horizontal axis (Fig. 6.3) In what follows, we shall refer to the normal probability density function as simply the “normal curve.” Asymptotic to the horizontal axis means that the normal curve extends from with its tails gradually approaching, but never touching, the horizontal axis. The normal probability distribution is completely determined once its mean and standard deviation are given. In this regard, if follows a normal distribution with a known mean and standard deviation, then we will write: