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Jack and Jill go to different schools. Jack got an 77 on a test with a mean of 60 and a standard deviation of 15. Jill got a 76 on a test with a mean of 60 and a standard deviation of 8. If both tests are graded on a curve, who did better?

Question

Jack and Jill go to different schools. Jack got an 77 on a test with a mean of 60 and a standard deviation of 15. Jill got a 76 on a test with a mean of 60 and a standard deviation of 8. If both tests are graded on a curve, who did better?

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Solution

To determine who did better, we need to calculate the z-score for each student. The z-score is a measure of how many standard deviations an element is from the mean.

For Jack:

  1. Subtract the mean from the score: 77 - 60 = 17
  2. Divide the result by the standard deviation: 17 / 15 = 1.13

So, Jack's z-score is 1.13.

For Jill:

  1. Subtract the mean from the score: 76 - 60 = 16
  2. Divide the result by the standard deviation: 16 / 8 = 2

So, Jill's z-score is 2.

Since Jill's z-score is higher, she did better on her test compared to her classmates than Jack did compared to his.

This problem has been solved

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Jack and Jill each scored 177 marks for their English and Maths exams. Both of their Maths marks add up to 153, what was the sum of their English marks?

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