Question

In recent years, SAT scores are approximately normal with a mean of 1100 and a SD of 130, while ACT scores are also approximately normal with a mean of 22 and a SD of 6.5. Without any studying, you took both tests and scored 1250 on the SAT and 24 on the ACT.Did you do better on the SAT or the ACT? Make sure to find the percentile (what percent of the test takers scored lower than you?) of each score and compare. b) You know you can do better, so you plan to spend the entire summer preparing to retake the SAT, and you’re aiming to score in the 97th percentile. What score will put you in the 97th percentile?

Answer 1

SAT score percentile Given that SAT scores are normally distributed with mean Ma 1100 and Standard deviation 0 2130 your score in SAT is 1250 2-sco de corresponding to a SAT score of 1250 = 1250-M 21250-1100 130 9 1.15 :: p(x <1250) = P(Z <1-15) - 0.8949 C Foom 2-table) :: percentage of test takers scored below you in SATIS 87-49% ACT Score percentile Given that ACT scores are nomally distributed with mean M= 22 and Standard deviation o -6.5 Your ACT score is 24. Z-score corresponding to an ACT score of 24 24-4 = 24-22 6.5 = 0.3076 0:31 :: PC* <24) P(Z <0:31) 20.6217 percentage of test takers scored below you in Act is 62.17% - co As the SAT percentile is better than the ACT percentile you scored better in SAT than in ACT, b) o z 130 Let Pay be the arth percentile Of SAT excam . SAT escam scores have H = z 11oo and Pan is the arth percentile = -21 99% of the scores are below Pay =) P[xc Pac] z score corresponding to Paya Batu 0.97.- Paz - 1100 =) 130 Zo such that 20 1.86 130 = 0.17 we need to find from a-table the value of P [z <30]0.99 Where zo Pan-1100 - 1-86 =) P97 = 1.86*130 +1100 (from table) score for SAT is 1342 130 Pan- 1100 130 = 1341.871342 ... gryth percentile