Question

The consumption of milk by individuals of a population is normally distributed. If you are a member of this population consuming milk, then: 1. If you have a standard score of Z = 2, what percentage of the population has scores greater than you? 2. If you have a standard score of Z = - 2, what percentage of the population has scores greater than you? 3. If you have a standard score of Z = 1, what percentage of the population has scores less than you? 4. If you have a standard score of Z = 1, what percentage of the population has scores farther away from the population mean (in either direction) than you? 5. If you have a standard score of Z = -1.7, what percentage of the population has scores farther away from the population mean (in either direction) than you? 6. If you have a standard score of Z = -1.7, what percentage of the population has scores greater than you?

Answer 1

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%.