Question

An instructor has graded 25 exam papers submitted by students in
a class of 26 students, and the average so far is 70. (The maximum
possible score is 100.) How high would the score on the last paper
have to be to raise the class average by 1 point?

By 2 points?

Answer #1

Case - 1: Average to be increased by 1 point:

Current average for 25 students = 70

Required average for 26 students = 71

Let the score of 26th exam paper is X. Then:

70*25 + X = 71*26

X = 71*26 - 70*25 = **96**

Case - 2: Average to be increased by 2 points:

Current average for 25 students = 70

Required average for 26 students = 72

Let the score of 26th exam paper is X. Then:

70*25 + X = 72*26

X = 72*26 - 70*25 = 122

But this is not possible because maximum marks one can get is
100. Hence, raising average by 2 points is **not
possible**.

2.27 Make-up exam: In a class of 27 students,
26 of them took an exam in class and 1 student took a make-up exam
the following day. The professor graded the first batch of 26 exams
and found an average score of 84 points with a standard deviation
of 7 points. The student who took the make-up the following day
scored 64 points on the exam.
a) Does the new student's score increase or decrease the
average?
Increases
Decreases
b)...

1. There are 52 students in your class. The top 26 students
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