Senior Math Award

The SAT and ACT are exams used by colleges and universities to evaluate undergraduate applicants. The test scores for each exam are normally distributed. In 2005, the math portion of the SAT exam had a mean score of 520 with a standard deviation of 115. In 2005, the math portion of the ACT exam had a mean score of 20.7 with a standard deviation of 5.

The PLD Mathematics Department gives an award each year to the top senior math student. Because there are so many excellent students to choose from this year, the math teachers decided to give the award to the student with the top score on a college entrance exam.

After checking the exam results with the guidance office, the math department teachers discovered that the top scorer on the math portion of the ACT was Laura with a score of 30. They also discovered that the top scorer on the math portion of the SAT was Jason with a 720.

  1. At the Senior Awards Night, Mrs. Feeback will be handing out the awards for the math department, and she must place the order for the plaque soon. Determine the correct name to be placed on the plaque for the top senior math student at PaulLaurenceDunbarHigh School. Justify your answer.
  1. There is one more chance to take the ACT this year. You believe that you can beat Laura’s score on the ACT. Find the probability that your score is lower than Laura’s. Explain your results.
  1. There is also one more chance to take the SAT this year. Your friend believes that he can score higher than Jason on the SAT. Find the probability that your friend’s score is higher than Jason’s. Explain your results.

Senior Math Award

Scoring Guide and Rubric

  1. 2 point: Laura’s z-score:

2 point: Jason’s z-score:

2 points for justification: Laura’s name should go on the plaque because her z-score is higher. This indicates that Laura did better with respect to the ACT than Jason did with respect to the SAT.

6 points total:

  1. 4 points:

(1pts for z score – 1 pt for adding .5 – 2pt for correct answer)

2 point: There is a 96.86% chance that you will not beat Laura’s score.

6 points total:

  1. 4 points:

2 point: There is a 4.09% chance that your friend’s score will be higher than Jason’s score.

6 points total:

Points Awarded:

18 points = 4

14-18 points = 3

10-14 points = 2

5-9 points = 1

0-5 points = 0

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