Solve the problem. Round to the nearest tenth unless indicated otherwise.
-Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find P81, which separates the bottom 81% from the top 19%.
A) 0.291
B) 0.88
C) 66.6
D) 73.5

Question

Quizplus · Accepted Answer

We need to find the value of the score that separates the bottom 81% from the top 19%. 
Since the scores are normally distributed, we can use the standard normal distribution table to find the corresponding z-score. 
The z-score that corresponds to the 81st percentile is 0.88 (from the table or calculator). 
We can use the formula z = (x - mu) / sigma to find the corresponding score x:

0.88 = (x - 63.2) / 11.7

Solving for x, we get:

x = 73.5

Therefore, the score that separates the bottom 81% from the top 19% is approximately 73.5.

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