Answer to Question #169843 in Statistics and Probability for lomii

Question

The score of Entrance Examination takers who took a 600 item exam resemble a normal distribution with a mean of 220 and a standard deviation of 10. The coordinator would like to get the lowest 15% of the scores and invite them for a retake examination. What range of scores indicates the inclusion in the retake of the exam?

Answer 1

We need to find the 15_th percentile of normal distribution with parameters 220 and 10. Let z = (x - 220) / 10 which is normally distributed with parameters 0 and 1. The 15_th percentile of z is equal to -1.03 , so x = -10*1.03 + 220 = 209.7. Hence the score that less or equal to 209.7 indicates the inclusion in the retake of the exam.