The grade of a course is based on two exams: the midterm and the final, each of 100 points maximum and counts 50% of the grade. The professor grades the midterm by randomly assigning each student a score independently of other scores of mean 73 and standard deviation (which is the square root of the variance) of 15. The professor grades the final by randomly assigning each student a score independently of other scores of mean 68 and standard deviation of 10. The number of students in the class is 64. 1. Estimate the probability that the midterm class average is 70% or more.
2. Estimate the probability that the final class average is 70% or more.
3. Estimate the probability that the course class average is 70% or more.
Use the Central Limit Theorem. Give numerical answers.

1. credits

2. dual - aspect

hope i : )

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation:

it will be a cylinder. with a diameter of 8 and 4 single pieces high