Students in ECON 122 (Econometrics) take a mid-term and final exam that accounts for 40 and 60 percent of their course grade respectively. Letandbenormally distributedrandomvariablesindicatingthe mid-term score and course score of each student, respectively, with

E() =79Std() =5

E() =65Std() =9

The correlation between scores on the mid-term and final exam is 0.75.

1.What is the percentage of students whose mid-term score is higher than75?

2.What is the probability that a student will score less on the final exam than the mid-term exam?

3.If a student scores 80 points on the midterm exam, what is their predicted score for the class?

4.The Economics Department recommends that students between the 5^thand 50 percentiles receive B- to B+ grades. If a student receives 70 points on the midterm exam, what is the probability that they will receive at least a B- grade for the class?