Answer:
1. 2.28%
2. 97.72%
3. 84.13%
4. 31.74%
5. 8.92%
6. 95.54%
Explanation:
1. A z score of 2 means has a proportion of the population of 0.9772 below
Therefore, the percentage of the the population that have an higher score = (1-0.9772)×100 = 2.28%
2. A z score of -2 means the percentage of the the population that have an higher score = (1-0.0228)×100 = 97.72%
3. A z score of 1 means the percentage of the the population that have a lesser score = (0.8413)×100 = 84.13%
4. A z score of 1 means the percentage of the the population that have a higher score = (1-0.8413)×100 = 15.87%
The population that have a lesser z score than -1 = 0.1587×100 = 15.87%
Therefore. the total percentage of the population that has scores farther away from the population mean in either direction = 2 × 15.87 = 31.74%
5. Where the z score = -1.7, we have;
The proportion lesser = 2×0.0446×100 = 8.92%
6. The percentage of the population that has a z score > -1.7 is presented as follows;
The proportion that have a z-score<-1.7 = 0.0446
Therefore, the proportion of the population that have a z-score more than -1.7 = 1 - 0.0446 = 0.9554
Hence the percentage of the population that has a higher z-score = 100×0.9554 = 95.54%.
