Question

A test has an overall mean of 150 and a standard deviation of 8.50. The distribution of scores for each sub-set is often closely approximated by the normal curve. What percentage of students will score lower than 142 or better than 158?

Answer 1

µ = 150

sd = 8.5

                                        

                                         = P(-0.94 < Z < 0.94)

                                         = P(Z < 0.94) - P(Z < -0.94)

                                         = 0.8264 - 0.1736

                                         = 0.6528

P(X < 142 or X > 158) = 1 - P(142 < X < 158)

                                    = 1 - 0.6528

                                    = 0.3472

                                    = 34.72%