Mary is predicted to score 150 on an achievement test in which the mean is 130 and the standard deviation is 20.

Question

I need help figuring out how to solve this.

 

35. Mary is predicted to score 150 on an achievement test in which the mean is 130 and the standard deviation is 20. Approximately how likely is it that her actual score will be above 158 if the coefficient of determination between the predictor and the achievement test is .84?

Answer 1

P(X>158) = 1 - P(X<=158) = 1 - P(z < (158-130)/20)

 

                                         = 1 - P(z < 28/20)

 

                                        = 1 - P(z < 1.4)

 

                                       = 1 - 0.9192

 

                                        = 0.0808  = 8.08%