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Answer :
Final answer:
The 65th percentile of SAT scores is approximately 1083.
Explanation:
The subject this question pertains to is mathematics, specifically the part dealing with normal distribution and percentiles. The SAT scores are said to be normally distributed with a mean of 1059 and a standard deviation of 89.
To find the 65th percentile of these scores, we first need to convert the percentile to a z-score.
A z-score is a measure of how many standard deviations an element is from the mean. In general, the the percentile to z-score conversion can be done using standard tables or a calculator. The z-score for the 65th percentile is approximately 0.385.
Now, we use the formula for the z-score which is X = μ + Zσ.
Substituting the given values, X = 1059 + 0.385*89 ≈ 1083.
Therefore, the 65th percentile of all SAT scores is approximately 1083.
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