Suppose that a college student is taking three courses: a two-credit course, a three-credit course, and a four-credit course. The expected grade in the two-credit course is 3.5, while the expected grade in the three- and four-credit courses is 3.0. What is the expected overall grade point average for the semester? (Remember that each course grade is weighted by its share of the total number of units.)

Answer:[tex] \bar X = \frac{\sum_{i=1}^n X_i w_i}{\sum_{i=1}^n w_i}[/tex]And replacing we got:[tex] \bar X= \frac{2*3.5 +3*3.0 +4*3.0}{2+3+4}= \frac{28}{9}=3.11[/tex]So then we expect an overall grad of 3.11 with those values. Step-by-step explanation:For this cae we have the following infoCredits   Grade  2             3.5  3             3.0  4             3.0Let X represent the grades and w, the weights(credits) we can find the expected overall grade with the following formula:[tex] \bar X = \frac{\sum_{i=1}^n X_i w_i}{\sum_{i=1}^n w_i}[/tex]And replacing we got:[tex] \bar X= \frac{2*3.5 +3*3.0 +4*3.0}{2+3+4}= \frac{28}{9}=3.11[/tex]So then we expect an overall grad of 3.11 with those values.

Given Information:Grade in two-credit course = 3.5Grade in three-credit course = 3.0Grade in four-credit course = 3.0Required Information:Expected GPA = ?Answer:Expected GPA = 3.11Step-by-step explanation:The overall expected GPA is basically the mean or averageE(X) = μ = Sum of grades/Total credit hoursSum of grades = ∑ weight*gradeSum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28Total credit hours = 2 + 3 + 4 = 9E(X) = μ = Sum of grades/Total credit hoursE(X) = μ = 28/9E(X) = μ = 3.11Therefore, the expected overall grade point average of this student for the current semester is 3.11