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Chapter 4: Problem 14

An instructor has graded 19 exam papers submitted by students in a class of 20 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?

Short Answer

Expert verified
The score on the 20th paper would need to be 90 to raise the class average by 1 point to 71, and 110 to raise the average by 2 points to 72. However, as the maximum possible score is 100, it's not possible to obtain an average of 72.

Step by step solution

01

Calculate the Total Score of 19 Students

Multiply the average score so far (70) by the number of students graded (19) to get the total score. This is done with the formula:\[ totalScore = averageScore * numberOfGradedStudents \]Substituting the given values gives:\[ totalScore = 70 * 19 \]
02

Find the Score Needed to Raise the Average to 71

To find the score the 20th student needs to achieve to raise the class average to 71, set the total score for all the students to 20 * 71, and subtract the total score of the first 19 students. This can be calculated with the formula:\[ requiredScore = (averageScoreDesired * totalStudents) - totalScoreOfDayOne \]Substitution gives: \[ requiredScore = (71 * 20) - (70 * 19) \]
03

Find the Score Needed to Raise the Average to 72

Using a similar approach as in Step 2, to calculate the score needed to increase the average to 72 substitute 72 in place of 71 in the formula:\[ requiredScore = (72 * 20) - (70 * 19) \]

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