Standardized entrance tests are often used in making admissions decisions for universities. A study of 1000 students completing a degree at a large university shows the following results. The students had an average score of 72 on the entrance exam with a standard deviation of 12. Final GPAs (GPAs at graduation) averaged 2.8 with a standard deviation of 0.4. The correlation between entrance test score and final GPA is 0.5.

A. Predict the final GPA of a graduating student whose entrance score is 90. [3 marks]

B. What percentage of variation in final GPA is explained by the entrance test score? [1 mark]

C. Suppose I wanted to guess the entrance test score for a student whose final GPA was 3.5. What is the slope of the relevant regression line? [2 marks]

D. A test preparation company offers a service to help you do better on the entrance exam. They promise that in addition to helping you get in to the university, a better score on the exam will ensure you have a better graduating GPA because of the positive correlation. Criticize this claim; be specific. [2 marks]

Can anyone please solve these problems with explanation.

I highly appreciate it thanks!