How to find the normal distribution How is the normal distribution calculated?

A normal distribution can be generated using the normal test in the miniab or with random data.

See for yourself, I still want you to give some points. Hee-hee......

The normal distribution formula <>

The density curve of the normal distribution function can be expressed as: x obeys the normal distribution, denoted as x n(m, s2), where is the mean, s is the standard deviation, x (-the standard normal distribution is 0, and s is 1. <>

The additivity formula for the normal distribution is: x+y n(3,8).

The linear combination of normal variables that are independent of each other obeys a normal distribution.

i.e. x n(u1,(q1) 2), y n(u2,(q2)) then z=ax+by n(a*u1+b*u2,(a 2)*(q1) 2+(b 2)*(q2) 2).

Standard Normal Distribution Density Function Formula: <>

The normal curve is bell-shaped, low at both ends and high in the middle, symmetrical to the left and right, because its curve is bell-shaped, so people often call it a bell-shaped curve.

If the random variable x obeys a normal distribution with a mathematical expectation of and a variance of 2, it is denoted as n( ,2). Its probability density function is the expected value of the normal distribution that determines its position, and its standard deviation determines the amplitude of the distribution. The normal distribution at =0, 1 is the standard normal distribution.

Graphical Feature: Concentration: The peak of the normal curve is at the positive **, that is, where the mean is located.

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

Uniform variability: The normal curve starts at the place where the mean is located and gradually decreases evenly to the left and right sides.

The area between the curve and the horizontal axis is always equal to 1, and the probability of integrating from positive infinity to negative infinity is 1, which is equivalent to the probability of the function of the probability density function. That is, the sum of the frequencies is 100%.

Normal distribution probability calculation formula: f(x)= x- ) Normal distribution is also called "normal distribution", also known as Gaussian distribution, the normal curve is bell-shaped, low at both ends, high in the middle, symmetrical left and right because its curve is bell-shaped, so people often call it a bell-shaped curve.

Main features: Estimating the frequency distribution A variable that obeys a normal distribution can estimate the proportion of frequencies in any value range according to the formula as long as the mean and standard deviation are known.

The normal distribution method is suitable for indicators that obey a normal (or near-normal) distribution, as well as those that can be converted to a normal distribution.

The percentile method is often used as an indicator of skewed distributions. The unilateral and bilateral cut-offs of the two methods in Table 3-1 should be mastered proficiently.

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 as the upper and lower control value. This is done on the basis that the measurement (or experimental) error follows a normal distribution under normal circumstances.

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

This is the standard normal distribution.

Density function: <>

If you are calculating probability, you need to use a distribution function.

However, its distribution function cannot be written as a normal analytic formula. The general calculation method is to calculate the value of the distribution function of the standard normal distribution function at each point to make a table, and find the probability by looking up the table in the actual calculation. The non-standard normal distribution function can be converted into a standard normal distribution and then calculated.

Parameter Meaning:The normal distribution has two parameters, i.e., expectation (mean) and standard deviation, with 2 being the variance.

A normal distribution has two parameters and a continuous random variable of 2.

, the first parameter is the late mean of the random variable that obeys the normal distribution, and the second parameter 2 is the variance of this random variable, so the normal distribution is denoted as n( ,2).

is a positional parameter of the normal distribution, which describes the position of the normal distribution of the concentration of oranges. The probability law is that the probability of taking a value that is close to is high, and the probability of taking a value that is farther away is smaller. The normal distribution is axed with x= as the axis of symmetry.

The left and right sides are perfectly symmetrical. Expectation, mean, median of normal distribution.

If the mode is the same, it is equal to .

The above content reference: Encyclopedia - Normal Distribution.

Solution: Use " (denotes the value of the standard normal du distribution function n(0,1)】x n(3,4), x-3) 2 n(0,1). Deficient.

1)p=p(x>2)+p(x<-2)。

and p(x>2)=p[(x-3) 2>(2-3) 2=-1 2]=1- (1 2)= 1 2); p(x<-2)=p[(x-3)/2<(-2-3)/2=-5/2]=φ5/2)=1-φ(5/2)。

Check the standard normal distribution.

Table (1 2) =

p=φ(1/2)+1-φ(5/2)=。

2)p=p[(x-3)/2>(3-3)/2=0]=1-φ(0)。and (0)=1 2, p=1-1 2=1 2.