The standard normal curve-how to use
What is the standard normal curve?
The standard normal curve is a curve that can be generated by a function, an equation. It is bell-shaped, symmetrical, its mean is 0, and it has three standard deviations.
The equation that generates the standard normal curve is:
$$y={{1\overσ\sqrt{2π}}}e^{-{(χ-μ)^2}\over2σ^2}$$
The surface area between two standard deviations can be calculated. Study the graphs below and always remember them. They are the basis of all other distributions (t-distribution, F-distribution).
Note that on each side of the mid point of the x-axis is the mean On each side of the mean there are 3 standard deviations (deviations from the mean). It is possible to calculate the area of the surface of the curve between the any two standard deviations.
It is very important to remember that:
between standard deviation +1.96 and -1,96 the percentage of the curve is 95%
between standard deviation +2.58 and -2.58 the percentage of the curve is 99%
How is the standard normal curve used?
Normal distribution, use number 1.
To describe, to organize data.
Normal distribution, use number 2.
Making statements of
probability, betting.
Normal distribution, use number 3.
To make statements regarding the reliability of a single mean.
Normal distribution, use number 4.
To make statements regarding the reliability of the difference between two means. .... next
