1. Students wishing to gain entrance to universities and colleges in the United States must complete the SAT Reasoning Test(1) There are three parts to the test: Writing, Mathematics and Critical Reading. Each part of the test has a mean of approximately 500, a standard deviation of 100 and is well modeled by the normal distribution. Answer the following questions based on these results. (a) Three students wrote their SATs and obtained the following scores. Determine their percentile for each part of the test. Name Writing Mathematics Critical Reading Joseph 450 642 579 Kaylyn 745 562 629 Larissa 327 437 575 (b) Sometimes the total score is used. In 2006, the mean total score was 1518 and the standard deviation was 308. Determine the percentile rank for each of these students. (c) Based on the total score, X ~ N(1518, 3082), a University has required that students who would be considered for acceptance must score at least 2000 on the SAT Reasoning Test. What proportion of students would score 2000 or higher? . (d) In order to gain acceptance to a particular College program, prospective students must be at the 87 percentile in Writing, the 90th percentile in Critical Reading and the 75th percentile in Mathematics. Determine the minimum scores that students need to meet these requirements