Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find $P _ { 81 }$ , which separates the bottom 81% from the top 19%.
A) 0.291
B) 66.6
C) 73.5
D) 0.88

Question

Quizplus · Accepted Answer

We can use the inverse normal distribution function on a calculator to find the z-score associated with the 81st percentile: 
invNorm(0.81) = 0.8779 
Now we can use the z-score formula to find the corresponding raw score: 
z = (x - μ) / σ 
0.8779 = (x - 63.2) / 11.7 
x = 73.5 
Therefore, the score that separates the bottom 81% from the top 19% is 73.5. The answer is choice C.

Scores on a Test Are Normally Distributed with a Mean P81P _ { 81 }P81​

Scores on a Test Are Normally Distributed with a Mean $P _ { 81 }$