Answer to Question #199498 in Statistics and Probability for Soini

Question

Test marks (%) obtained in a test are normally distributed with a mean of 55% and variance of 400(% squared). What is the probability that a randomly selected student scored above 60%?

Answer 1

$\mu =55 \\ \sigma = \sqrt{400} = 20 \\ P(X>60) = 1 -P(X<60) \\ =1 -P(Z< \frac{60-55}{20}) \\ = 1 -P(Z<0.25) \\ = 1 -0.5987 \\ = 0.4013$