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Answer :
A student's SAT score corresponding to the 65th percentile in a normally distributed set with a mean of 1019 and a standard deviation of 200 is 1097.
to find the SAT score corresponding to the 65th percentile in a normally distributed set with a mean of 1019 and a standard deviation of 200, you need to use the Z-score table.
The Z-score associated with the 65th percentile is approximately 0.39. Using the Z-score formula:
Z = (X - μ) / σ
We rearrange to solve for X (the SAT score):
X = Z * σ + μ
Plugging in the values:
X = 0.39 * 200 + 1019
X = 78 + 1019
X = 1097
Therefore, the SAT score at the 65th percentile is 1097.
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