Scores on a test have a mean of 71 and $Q _ { 3 }$ is 82 . The scores have a distribution that is approximately normal. Find P90. (You will need to first find the standard deviation.)
A) 90.4
B) 92.7
C) 91
D) 92

Question

Scores on a test have a mean of 71 and $Q _ { 3 }$ is 82 . The scores have a distribution that is  approximately normal. Find P90. (You will need to first find the standard deviation.)
A) 90.4
B) 92.7
C) 91
D) 92

Quizplus · Accepted Answer

To find P90, we first need to find the standard deviation. In a normal distribution, Q3 corresponds to the 75th percentile. Using the Z-score for the 75th percentile (approximately 0.675), we can calculate the standard deviation: $ \sigma = \frac{82 - 71}{0.675} \approx 16.3 $. Then, using the Z-score for the 90th percentile (approximately 1.28), we find P90: $ P90 = 71 + 1.28 \times 16.3 \approx 92 $.

Scores on a Test Have a Mean of 71 And Q