Answer :
The score that separates the top 59% from the bottom 41% is 39.3.
To solve this problem, we need to find the z-score that separates the top 59% from the bottom 41%, and then use the z-score formula to find the corresponding raw score.
The z-score for the top 59% is the z-score that corresponds to a cumulative area of 0.59 to the left of it. We can find this using a standard normal table or a calculator:
z = invNorm(0.59) = 0.24
The z-score for the bottom 41% is the z-score that corresponds to a cumulative area of 0.41 to the left of it:
z = invNorm(0.41) = -0.24
The score that separates these two z-scores can be found using the z-score formula:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation. Solving for x, we get:
x = z * σ + μ
Plugging in the values we found earlier, we get:
x = 0.24 * 7.6 + 37.6 = 39.3
Therefore, the score that separates the top 59% from the bottom 41% is 39.3.
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