Question

The mean and standard deviation of SAT math exam scores were 527 and 120, respectively, in 2017. Assume that the scores are normally distributed and answer the following questions. a. Find the 30th percentile. b. If your score is 700, what percentage of the students got higher scores than you in 2017? c. What percentage of students got SAT math scores from 400 to 600? d. If your score is 650, what is the percentile of your score?

Answer 1

a) z score corresponding to 30th percentile = -0.52

Hence,

30th Percentile = 527 - 0.52*120 = 464.6

b) z score for 700 = (700 - 527)/120 = 1.44

P(z > 1.44) = 0.075

So,

7.5% students got higher score than you in 2017.

c) z score for 400 = (400 - 527)/120 = -1.06

z score for 600 = (600 - 527)/120 = 0.61

Hence,

Percentage of scores between 400 and 600

= P(-1.06 < z < 0.61)

= 0.5845

= 58.45%

d) z score for 650 = (650 - 527)/120 = 1.025

P(z < 1.025) = 0.8473

So,

Percentile = 85