Standard normal distribution + standard normal distribution probability table + distribution function + integral

Source: Internet
Author: User

X~n (μ,σ²): General normal distribution: mean μ, variance is σ²

For a standard normal distribution, there is a table called: Standard normal distribution table:

The table calculates the probability that P (x<=x) " one grumble at a [[email protected],x]". This is the area shown in the shadow graph below:

If x= is split into 1.9 and 0.06. Intersection of Axis 1.9 and longitudinal axis 0.06:0.975. is the probability of x<=1.96.

That is, the standard normal distribution graph and the X=a area are equal to the probability that x<=a ( a value falls on a certain interval of the group data ).

For example, for a group of score group data, the average value is 45 and the standard deviation is a 10 normal distribution:

So, to take a classmate's results, its score at more than 63 of the probability of " falling in [63,[email protected]" interval probability "?

This is the area of the diagonal line in the picture!

If f (x) is done [email protected] to 63 of the scoring, subtract it with 1. Scoring is more troublesome. Then, the Group data standardization, standardized data to comply with the standard overall distribution ~! Standardize the 63 data.

The 63 standardization is "distance/standard deviation"

(63-45)/10=1.8. That is, in the standard overall distribution, the probability that the score falls on the interval [1.8,[email protected]] is:


Also said, for the normal distribution, want to obtain the data interval probability (area), the "Split point" standardization can be, look up the table can!!

The following descriptions are equivalent:

All students, scores of more than 63 students accounted for 3.59%;

All students, the probability of taking a score greater than 63 points is 3.59%;

All students, any one score, the probability of the standard scoring is greater than 1.8 is 3.59%;

Standard normal distribution + standard normal distribution probability table + distribution function + integral

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