When testing for a difference between two population means using a -test, you obtain a -score of -2.15. What is the total area under the two tails on a normal curve?

0.8886

Step-by-step explanation:

A two-tailed normal curve is one where there’s an area in each of the two tails. To find the area for a two-tailed normal curve, you have to read a z-table.

Z-tables are lists of percentages. The total area under a normal curve is 100%(1.) and the area z-table lists as a fraction of that percentage. For example, you could look up a z-score for 60% of a normal curve (.6) or 6% (0.06).

If you are looking for other variations on finding areas under curves, see the area under a normal distribution curve index. The index lists several variations, like finding areas for right-tailed normal curves or left-tailed normal curves.

Step 1: Look in the z-table for one of the given z-values by finding the intersection. For this case, we are asked to find the area in the tail to the left of z = -2.15, lookup 2.15.* The table below illustrates the result for 2.15 (0.1 in the left-hand column and 0.05 in the top row. the intersection is 0.0557).

Step 2: Subtract the z-value you just found in step 1 from 0.500. In this case, we found 0.0557 as your z-value, then 0.500 – 0.0557 = 0.4443. Set this number aside for a moment.

Step 3: Repeat steps 1 and 2 for the other tail. For example, you might have symmetrical tails (that’s the most common spread for two-tailed problems). So if you repeat the steps you would get 0.4443 again.

Step 4: Add both z-values together. In this case, the two z-values are 0.4443 and .3228, so:

0.4443 + 0.4443 = 0.8886

Therefore, the total area under the two-tails on a normal curve is 0.8886

a. is correct