Use a table of z-scores and percentiles to find the percentage (to the nearest whole percentage) of data items in a normal distribution that lie between the following two z-scores.
z = 1 and z = 3
To find the percentage of data items that lie between two z-scores, we can use the standard normal distribution table. Specifically, we need to find the area (percentage) under the curve between the two z-scores.
Looking at the standard normal distribution table, we can find the areas corresponding to the z-scores of 1 and 3. The area listed in the table is the area to the left of the corresponding z-score.
For z = 1, the area to the left is 0.8413 or 84.13% (rounded to the nearest whole percentage).
For z = 3, the area to the left is 0.9987 or 99.87% (rounded to the nearest whole percentage).
To find the percentage between the two z-scores, we subtract the smaller area from the larger area:
99.87% - 84.13% = 15.74%
Therefore, approximately 15.74% of the data items in a normal distribution lie between z = 1 and z = 3.