Areas under the Normal Curve

You frequently need to know the Probability of something happening. If you can assume that your data come from a normal distribution, you can use this calculator.

Fill in the fields in the form below. You will calculate the Probability on your computer and display the results below.

We have begun with the data in the example in Question 53, BHA 6.9 to give you are starting point. Use your own data.

Your value to test (X)		-		Process average
	Standard Deviation

This gives a Z value of

The Probability of your value being less than Z is %

Notes

The Z value is a "standardized value". When you claculate it and use it, you assume that your data comes from a "Normal" distribution. This is a fair assumption when your data is a physical measurement (eg feet or meters). It is not a good assumption if your data is a count of something or it is a time measurement (eg time to arrive or time to do something).
We first calculate your Z value. Z standardizes your original value by subtracting the average and dividing by the standard deviation.

The probability of your value X being further away (less than) the average than Z is calculated. For example, the probability of Z being less than 1, is 84%. (Try X = 32, Average = 22 and Std Dev = 10).
On the other hand, the probability that Z is greater than 1.96 is 2.5%. (Try X =41.6. Average = 22 and Std dev = 10, which gives 97.5% less than X. So 2.5% (=100% - 97.5%) is greater than X.)
In the example used in Question 53 (BHA 6.9), we use X of 14, Average of 22 and Standard Deviation of 10 to obtain a Z value of -0.81. This gives a Probability of 21%. The negative sign tells us that everything is happening on the left hand side of the average. 21% of the distribution is to the left of specification. So, 79% (100% - 21%) is to the right of the specification.