Normal Distribution and Standard Normal Distribution

NORMAL DISTRIBUTION

In Statistic, distribution curve is the most common curve, which could be used to find the probability and z-scores. Using Calculus, we can find the function of this belly curve, which is:

To determine the probability of a certain event,we can find the Area under the Curve by taking the integral.

For those who haven't taken Calculus courses, there is a mechanical way to handle this problems, which is TI83/ TI84 calculator.
In the Calculator,
                                     Click 2nd --> VARS-->2: normalcdf (--> Enter (1)
The data in the parenthesis should be inserted in this following order :
                     
                            normalcdf (Boundaries of the probability, Mean, Standard Deviation)
This could give out the data directly.

STANDARD NORMAL DISTRIBUTION 
Moreover, we could turn this graph into Standard Normal Distribution curve, which means finding the z-score from the mean and standard deviation.

Using z-score, we could find the probability by following step (1). However, this time the ordering is different because the mean and deviation of standard is 0 and 1.
                            normalcdf (Boundaries of the probability)
NOTE: Enter E99 for the infinity and -E99 for negative infinity
It is interesting to know that the integral of the the function above will be 1 when the limits are infinity, which prove that the z-score will add up to 1.