Statistics Z scores and percentages

Question

Determine the following percentages for a z score of 0.90 (Round your answers to 2 decimal places) (6 marks) a. The percentage of scores fall below this z score. b. The percentage of scores fall between the mean and this z score. c. The percentage of scores above this z score.

Answer 1

If we use a z table or statistical calculator, we can find a z score of 0.9 corresponds to an area of 0.8159, or 0.82 if we round to two decimal places.

Part a) answer comes straight from this reading - 0.82, or 82% would be below this z score.

Part b) asks for what percentage of scores fall between the mean and the z score in part a. At the mean, the z score is 0. At a z score of 0, the area under the curve is 0.5. So the area between a z score of 0.9 and a z score of 0 is equal to 0.82-0.5 = 0.32, or 32%

Part c) asks for the percentage above the z score of 0.9. The area under the entire curve is 1 (not really but close enough for this). If the area under the curve when z = 0.9 is 0.82, then the area under the curve when z > 0.9 would be 1-0.82 = 0.18, or 18%

Let me know if something isn't clear and I'll try to explain it more clearly.