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Unformatted text preview: Statistics 21: Homework 3 Solutions 1. A student scores at the 90th percentile on a midterm examination. All previous semesters of the class have resulted in an approximately football shaped scatter plot of final exam scores versus midterm scores, and the historical correlation between these two quantities is consis- tently 0.8. Predict the students percentile on the final exam. We can answer this question in 3 steps: first, we will determine the students midterm score in standard units using the Normal distribution; second, we will predict the students final exam score in standard units using the regression equation; third, we will convert this predicted score to a percentile using the Normal distribution. Step 1: Although we dont know the students score, the football-shaped scatter plot ensures that the midterm scores follow a Normal distribution. We can therefore find the students score in standard units by finding the value of z that corresponds to the 90th percentile in the standard Normal distribution. Because 90% of the data are less than z , then 10% of the data are greater than z , so we have the right tail area. By the symmetry of the Normal distribution, the left tail area is also 10%, and therefore the middle region has area 80%. We can find z by locating the value in the table with an Area measurement closest to 80%; this is given by z = 1 . 3 with area 80 . 64%. Therefore, the student scored z = 1 . 3 standard deviations above the mean. We will call this value M = 1 . 3 to represent the midterm score in standard units; M N (0 , 1)....
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- Spring '08