suppose the correla tion between SAT Verbal scores and Math scores is .57 and that these scares are normally distributed. IF a student's Verbal score places her at the 90th percentile, at what percentile would you expect her Math scores to be?
To determine the percentile at which you would expect the student's Math score to be, considering the given information, we need to use the concept of z-scores and the cumulative distribution function (CDF) of the normal distribution.
Here are the steps to calculate the expected percentile of the Math score:
1. Determine the z-score corresponding to the 90th percentile in the standard normal distribution. The z-score can be found using a z-score table or a calculator. The z-score for the 90th percentile is approximately 1.28.
2. Use the correlation coefficient to compute the expected z-score for the Math scores. Since the correlation coefficient (r) is 0.57, we can multiply the z-score for the Verbal scores by the correlation coefficient: z_math = r * z_verbal = 0.57 * 1.28 = 0.7296.
3. Calculate the percentile corresponding to the expected z-score for the Math scores. The percentile can be determined using the z-score to percentile conversion table or an online calculator. The percentile corresponding to z_math = 0.7296 is approximately 76.04%.
Therefore, you would expect the student's Math score to be around the 76th percentile.