Question

The standard normal curve shown below models the population distribution of a random variable. What proportion of the values in the population does not lie between the two z-scores indicated on the diagram?

Z = -1.3
Z = 0.75

Answer 1

About 32.34% of the values do not lie between the z-scores of -1.3 and 0.75.

First, we need to find the region between the z-scores.

If you look at a normal distribution table, you will get the following values:

0.75 = 77.34%
-1.3 = 9.68%

Subtraction those gives us the area between the z-scores.
77.34 - 9.68 = 67.66%

Now, just subtract that value from 100% to get the amount outside of the area.
100 - 67.66 = 32.34%