About % of the area under the curve of the standard normal distribution is between z = − 3.045 z = - 3.045 and z = 3.045 z = 3.045 (or within 3.045 standard deviations of the mean).

Question

About % of the area under the curve of the standard normal distribution is between  and  (or within 3.045 standard deviations of the mean).

Answer 1

Finding the area under a standard normal distribution curve between 3.045 standard deviations of the mean will require finding the probabilities for both the positive value and negative values of the 3.045 standard deviations.

From the standard normal probabilities tables, positive z (3.045) results in a value half way between 0.9988 and 0.9989. That gives a result of 0.99885.

Negative z (-3.045) results in a value half way between 0.0012 and 0.0011. That gives a result of 0.00115

To get the area under a standard normal distribution curve between 3.045 standard deviations just subtract the negative z results from the positive z results.

Area = 0.99885 - 0.00115

Area under the standard normal distribution curve between 3.045 standard deviations = 0.9977