Answer :
Final answer:
Using the 68-95-99.7 rule, we can calculate the percentage of scores in each category. The percentages are as follows: a. 50% b. 15.87% c. 15.87% d. 97.72% e. 2.28% f. 84.13% g. 84.13% h. 68%.
Explanation:
To find the percentage of scores in each category, we can use the 68-95-99.7 rule. This rule states that for a normal distribution, approximately 68% of scores fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
a. To find the percentage of scores greater than 100, we can calculate the z-score of 100 using the formula z = (x - mean) / standard deviation. The z-score is (100 - 100) / 20 = 0. So, the percentage of scores greater than 100 is 50%.
b. We can use the same method to find the percentage of scores greater than 120. The z-score of 120 is (120 - 100) / 20 = 1. So, the percentage of scores greater than 120 is 15.87%.
c. To find the percentage of scores less than 80, we can calculate the z-score of 80. The z-score is (80 - 100) / 20 = -1. So, the percentage of scores less than 80 is 15.87%.
d. Using the same method, the z-score of 140 is (140 - 100) / 20 = 2. So, the percentage of scores less than 140 is 97.72%.
e. To find the percentage of scores less than 60, the z-score is (60 - 100) / 20 = -2. So, the percentage of scores less than 60 is 2.28%.
f. To find the percentage of scores less than 120, the z-score is (120 - 100) / 20 = 1. So, the percentage of scores less than 120 is 84.13%.
g. To find the percentage of scores greater than 80, the z-score is (80 - 100) / 20 = -1. So, the percentage of scores greater than 80 is 84.13%.
h. To find the percentage of scores between 80 and 120, we need to find the percentage of scores less than 120 and subtract the percentage of scores less than 80. So, the percentage of scores between 80 and 120 is 84.13% - 15.87% = 68%.
