Solve the problem. Round to the nearest tenth unless indicated otherwise.
-A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%.
A) 207.8
B) 211.3
C) 212.5
D) 187.5

Question

Quizplus · Accepted Answer

To find P60, we need to find the score that separates the lower 60% from the top 40%. This means that the area under the normal curve to the left of P60 is 0.60 and the area to the right of P60 is 0.40.
Using a standard normal distribution table, we find the z-score that corresponds to a cumulative area of 0.60 is approximately 0.25. 
Now we can use the formula: 
z = (x - μ) / σ 
where z is the z-score, x is the score we want to find (P60), μ is the mean (200), and σ is the standard deviation (50).

Plugging in the values we get:
0.25 = (P60 - 200) / 50

Solving for P60, we get:
P60 = 212.5

Therefore, the answer is C) 212.5.

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