Final answer:
To solve left z=-1.44 and right of z=2.21, use the z-table to find the area to the left of each z-score and then use 1 minus that area for the z=-1.44. For z=2.21, the area to the right is 1 minus the area to the left of z=2.21 as found in the z-table.
Step-by-step explanation:
The student has presented two z-scores for which we need to find the corresponding areas under the standard normal curve. Applying the z-table helps us determine these areas. For a left z-score of -1.44, we find the area to the left of the z-score and for a right z-score of 2.21, we need to find the area to the right, which can be calculated by subtracting the area to the left from 1, since the total area under the curve is 1.
To find the area to the left of a z-score, you find the corresponding value on the z-table, which generally gives you the cumulative probability up to that z-score. The z-table is set up so that the z-scores run down the left vertical axis, and the decimal portion of the z-score runs across the top horizontal axis.
Using the z-table, we look up the value for 1.44 (since the table typically only shows positive z-scores) and then subtract the corresponding value from 1 for the left z-score of -1.44. For the right z-score of 2.21, we directly find the corresponding area to the left from the table and subtract it from 1 to get the area to the right.