Scores on a test have a mean of 73 and $Q _ { 3 }$ is 80. The scores have a distribution that is approximately normal.
Find P90. (You will need to first find the standard deviation.)
A)86.4
B)85.7
C)86.8
D)85.3

Question

Quizplus · Accepted Answer

To find P90, we first need to determine the standard deviation. In a normal distribution, Q3 (the 75th percentile) is approximately 0.675 standard deviations above the mean. Given Q3 = 80 and mean = 73, the standard deviation is approximately (80 - 73) / 0.675 = 10.37. For P90, which is 1.28 standard deviations above the mean, we calculate 73 + 1.28 * 10.37 ≈ 86.4.

Scores on a Test Have a Mean of 73 And Q