Answer to Question #340177 in Statistics and Probability for jay

Question

Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17. Carlos has two more 20-point homework assignments to complete before his progress report gets sent out, and he wants to raise his mean score to an 18. Is it possible for Carlos to raise his mean score to an 18? If it is possible, explain what scores he would need to get, and if not, explain why not.

Answer 1

The total score for 8 math homework assignments is $17(8)=136$ points.

The possible maximum score for 2 additional math homework assignments will be $20(2)=40$ points.

Then possible maximum score for $8+2=10$ math homework assignments

will be $136+40=176$ points.

The possible maximum mean score will be $\dfrac{176}{10}=17.6<18.$

Therefore it is not possible for Carlos to raise his score to an 18.