Answer :
Final answer:
The SAT score problem involves calculating z-scores, identifying scores at certain standard deviations above the mean, and comparing results across different standardized tests by converting scores to a common scale.
Explanation:
The SAT scores and related statistics problems can be solved using concepts of normal distribution and statistical testing. A point estimate is a single value estimate of a population parameter. In part A, for example, with 35 out of 124 students scoring less than 530, the point estimate would be the proportion, which is 35/124. A confidence interval gives a range of values for our parameter based on the sample statistic and is useful for making inferences about the population parameter. The standard deviation is a measure of the amount of variation or dispersion of a set of values, and the hypothesis test is a method of making decisions or inferences about population parameters.
To calculate the z-score for an SAT score of 720, you would use the formula z = (X - µ) / σ, where X is the score, µ is the mean, and σ is the standard deviation. Using the 2005 data where µ = 520 and σ = 115, the z-score for an SAT score of 720 is z = (720 - 520) / 115 ≈ 1.74. This z-score tells us that 720 is 1.74 standard deviations above the mean.
To find a score that is 1.5 standard deviations above the mean of 520, you multiply 1.5 by the standard deviation of 115 and add it to the mean: 520 + 1.5(115) ≈ 692.5. This score is higher than the average SAT math score.
Comparing scores across different tests such as the SAT and ACT would involve converting scores to a common scale like z-scores or percentiles to determine who performed better relative to others taking the same test.
Learn more about SAT Math Scores here:
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