As can be seen from the histogram drawn by the frequency table data of general distribution, the peak value is located in the middle, and the left and right are roughly symmetrical. We assume that if the number of observation cases is gradually increased and divided into groups, the connecting line at the top of the histogram will gradually form a smooth curve, with the peak at the center (where the mean value is located), and the two sides will gradually decrease and be symmetrical, and will not intersect with the horizontal axis. This curve is called frequency curve or frequency curve, which is similar to normal distribution in mathematics. Since the sum of frequencies is 100% or 1, the area on the horizontal axis under the curve is 100% or 1.

For the convenience of application, the normally distributed variable X is often transformed. This transformation transforms the original normal distribution into the standard normal distribution, also known as the U distribution. U is called standard normal variable or standard normal deviation.

In practical work, it is often necessary to know the percentage of the area of an interval on the horizontal axis under the normal curve to estimate the percentage (frequency distribution) of the number of cases in this interval to the total number of cases or the probability that the observed value falls within this interval. The area of an interval under a normal curve can be obtained from the table 1 For data with normal or near normal distribution, if the mean and standard deviation are known, the frequency distribution can be roughly estimated.

Normal distribution, also called normal distribution, is a probability distribution of continuous random variables. A large number of phenomena in nature, human society, psychology and education are distributed according to formal forms, such as the level of ability and the quality of students' grades. It has different distribution patterns with the size and unit of the mean and standard deviation of random variables. Standard normal distribution is a kind of normal distribution, and its mean value and standard deviation are fixed, with the mean value of 0 and the standard deviation of 1.