Scores on a test have a mean of 70 and P75 is 82 The scores

Scores on a test have a mean of 70 and P75 is 82. The scores have a distribution that is approximately normal. Find P90

Solution

P3 means 75%, that is a z of ~0.67

Now, 82 – 70=12, so the standard deviations is 12/0.67=17.9.

now find the z that represents a score of 90

90 - 70 is 20

20 / 17.9 = 1.11

from a z-table, a z of 1.11 represents a probability of 84.38%..