N(0，σ？ )+C ~ N(C，σ？ )。

A random variable conforms to the normal distribution, and we can draw its function image. Adding a constant to each number will only make the function image move left and right, then it will only change the expected value, still conform to the normal distribution, and even the standard deviation will not change.

Extended data:

Some properties of 1. normal distribution;

1, concentration: the peak of the normal curve is located in the center, that is, where the average value is located.

2. Symmetry: The normal curve is centered on the mean value, which is symmetrical left and right, and both ends of the curve never intersect with the horizontal axis.

3. Uniform variation: the normal curve starts from the place where the mean value is located and gradually decreases evenly to the left and right sides respectively. The area between the curve and the horizontal axis is always equal to 1, and the probability of the function equivalent to the probability density function integrating from positive infinity to negative infinity is 1. That is, the sum of frequencies is 100%.

4. Regarding μ symmetry, the maximum value is taken at μ, the value is taken at positive (negative) infinity, there is an inflection point at μ σ, the shape is high in the middle and low on both sides, and the probability density function curve of normal distribution is bell-shaped, so people often call it bell-shaped curve.

Second, the application of normal distribution curve

1. Estimation of frequency distribution As long as the mean and standard deviation of a variable subject to normal distribution are known, the frequency proportion in any range can be estimated according to the formula.

2. Quality control: In order to control the measurement (or experiment) error in the experiment, it is often used as the upper and lower warning value and the upper and lower control value. The basis of this is that under normal circumstances, the measurement (or experimental) error obeys the normal distribution.

3. Normal distribution is the theoretical basis of many statistical methods. Many statistical methods, such as test, variance analysis, correlation and regression analysis, require that the analyzed indicators obey normal distribution. Although many statistical methods do not require the analysis indicators to obey normal distribution, the corresponding statistics in large samples are approximately normal distribution, so these statistical inference methods are also based on normal distribution.

Baidu Encyclopedia-Normal Distribution