Given a standardized test that is normally distributed with mean of 80 and standard deviation of 12 what is P(X < 62) and What is the score of an individual that represents the 13th percentile?

Answer 1

X~N(80, 144) where μ = 80 and σ = 12.

z = (62 - 80)/12 = -18/12 = -1.5

P(X < 62) = P(z < -1.5) = 0.0668

13th percentile means that 13% of students did worse than that individual on the standardized test.