Standard Normal Distribution Areas

z

1

-0.67

z

2

4.5

complement

This Demonstration provides a dynamic supplement to elementary statistics textbooks that show how to use a table of standard normal cumulative probabilities. As you slide

z

1

along, holding

z

2

fixed at the upper limit, these probabilities are obtained as the area shown under the curve. Moving

z

2

to the left, the upper area probability is added to the area to the left of

z

1

. The probability corresponding to the interval between

z

1

and

z

2

is obtained by taking the complement.

You can see that the probability corresponding to the interval

(-0.67,0.67)

is close to 0.5.

This Demonstration also illustrates the 68–95–99.7 rule that, in a normally distributed population, about 68% of the observations fall within one standard deviation, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.