Final answer:
For a normal distribution of scores, the proportion of scores falling above or below specific Z scores can be determined using a Z-table or a statistical software. The proportions are: a. About 68 percent, b. About 95 percent, c. About 99.7 percent, d. Approximately 0.0228, and e. Approximately 0.6826.
Step-by-step explanation:
a. About 68 percent of the values lie between z-scores of -1 and 1.
b. About 95 percent of the values lie between z-scores of -2 and 2.
c. About 99.7 percent of the values lie between z-scores of -3 and 3.
d. To find the proportion of scores below a Z score of -2.00, you would need to find the proportion above that z-score and subtract it from 1. Since the area under the normal curve sums up to 1, subtracting the proportion above -2.00 from 1 would give you the proportion below -2.00. By using a Z-table or a statistical software, you can find that the proportion above a Z score of -2.00 is about 0.9772. Therefore, the proportion below a Z score of -2.00 is approximately 1 - 0.9772 = 0.0228.
e. To find the proportion of scores between Z scores of -1.00 and 1.00, you would need to find the proportion above a Z score of -1.00 and subtract it from the proportion above a Z score of 1.00. By using a Z-table or a statistical software, you can find the proportion above a Z score of -1.00 is about 0.8413 and the proportion above a Z score of 1.00 is about 0.1587. Therefore, the proportion between Z scores of -1.00 and 1.00 is approximately 0.8413 - 0.1587 = 0.6826.