Must be done in Java.

You are to build a grading app for an instructor who needs to enter

1. Exam #1 Score (0 50 points),
2. Exam #2 Score (0 50 points),
3. Exam #3 Score (0 50 points),
4. Exam #4 Score (0 50 points),
5. Assignment #1 Score (0 75 points),
6. Assignment #2 Score (0 75 points),
7. Assignment #3 Score (0 75 points),
8. Assignment #4 Score (0 75 points).

After entering all the scores, the maximum scores one student can get is 500. Based on the criteria given below, print the grade for the instructor.

FinalScore >= 450 : A, FinalScore> =400: B, FinalScore> =350: C, FinalScore>= 300: D, Else : F.

However, since the instructor is very generous, he wants to give better grades to the students based on the statistics of the students (this is an example only, not an actual case with you!).

Say, the distribution of the total points of 10 students are

400

350

370

280

300

290

310

340

350

330

Then, the criterion of the grade A is

A: >= Average of the students + (2 Standard Deviation of the students)

B: >= Average of the students + (1 Standard Deviation of the students) (but less than A)

C: >= Average of the students (but less than B)

D: >= Average of the students (1 Standard Deviation of the students) (but less than C)

F: < Average of the students (2 Standard Deviation of the students)

There is a catch for this assignment. The thing is that the mean and the standard deviation sometimes do not exactly cover the entire system. Say your mean is 50 and your standard deviation is only 2.5. Then, however you do, you cannot clearly divide between A and B, B and C because doubling only covers up to 5. So, C is between 55 and 45. There will be some gaps. What about too much standard deviation? Say, it is 10. Then, there will be some overlaps. So, the trick is depending on the standard deviation and the mean, try to regulate those values accordingly so that there may not be either gaps or overlaps. That is a genuine way of programming based on the situation.