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In 2019 the Math SAT scores in a state averaged 510 points, with an SD of about 120 points. The histogram of the scores followed the normal curve reasonably well. One Math SAT test-taker scored 0.53 SD above average. About what percentage of test-takers had lower scores than she did?

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Final answer:

A student scoring 0.53 SD above the mean on the normal distribution of SAT scores typically ranks around the 70th percentile, which means approximately 70% of test-takers had lower scores.

Step-by-step explanation:

The student who scored 0.53 SD above the average on the Math SAT test wants to know the percentage of test takers who had lower scores than she did. Since the SAT scores are normally distributed, we can use the properties of the standard normal distribution to answer this question.

When scores are normally distributed, a score that is 0.53 standard deviations above the mean corresponds to a specific percentile in the distribution. We can use the standard normal distribution table or a calculator with statistical functions to find the percentile ranking of a score that is 0.53 SDs from the mean.

In the standard normal distribution, a z-score of 0.53 corresponds to approximately the 70th percentile. This means that about 70% of test-takers scored lower than the student in question.

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