Question

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. you find an individual that reads 57.1 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 95 words per minute and a standard deviation of 21 words per minute. At what percentile is the child's reading level?

Answer 1

Percentile Rank for 57.1 Normal Distribution mu = 95 sigma = 21 percentile Rank is equal to 100 * P(X < 57.1) we convert this to standard normal using z = (X - mu)/(sigma) z = (57.1 - (95))/21 approx -1.804762 approx -1.80 P(Z < -1.80) = Area to the left of -1.80 P(X < 57.1) = P(Z < -180) = 0.0359 (from z-table) Here percentile rank = 100 * 0.0359 = 3.59 Percentile Rank for 57.1 is 3.59 approx 4th Exact using excel function normdist (57.1, 95, 21, 1) or TI'sfunction normal - cdf (lower, upper, mean, std/sqrt(n)) answer is: 3.555597402394830