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%.
(1 point)
Responses
207.8
211.3
212.5
187.5
To find the score that separates the lower 60% from the top 40%, you can find the z-score associated with the 60th percentile and use it to find the corresponding score.
First, find the z-score corresponding to the 60th percentile by using the z-table or a calculator. The z-score for the 60th percentile is approximately 0.2533.
Next, use the formula for z-score: z = (X - μ) / σ, where X is the score we want to find, μ is the mean (200), and σ is the standard deviation (50).
Plug in the values and solve for X:
0.2533 = (X - 200) / 50
0.2533 * 50 = X - 200
12.665 = X - 200
X = 212.665
Round to the nearest tenth, the score that separates the lower 60% from the top 40% is approximately 212.5.
Therefore, the answer is:
212.5