The normal probability distribution is the most important continuous probability distribution. This is the case for two reasons. The first is that there are many real-world applications such as height, weight, test scores, rainfall and others. Second, it is extensively used in the field of statistical inference, which include important topics like confidence intervals and hypothesis testing. The graph of the normal distribution, called the normal curve, has a bell-shape. It is differentiated by two parameters, the mean and standard deviation. The mean is the highest point on the normal curve and the standard deviation determines how flat and wide the curve is.
The standard normal probability distribution is a normal probability distribution with a mean of 0 and standard deviation of 1. When working with the standard normal distribution, the letter z is used to denote the random variable instead of x. There are three types of probability we must know how to compute for the standard normal distribution. The first is the probability that z will be less than or equal to a value. The second is the probability that z will be between two values. The third is the probability that z will be greater than or equal to some value. All three of these probabilities can be computed by using the standard normal distribution, or z, table. From here, it is straightforward to calculate probabilities for any normal probability distribution