To determine whether Fiona can pass with merit, you must see if a mean of 52% can be increased to 60% by the highest possible score (which is 100% in this case). Remember, mean is the average (all scores added together, divided by the number of scores). In this case, we were given the following information: the mean of 7 scores is 52%, and asked if it is even possible for Fiona to pass with merit. Therefore, our second mean is the mean of one score, which is 100%. Let x represent her score. Here's the math:
52/100 = 7/8x 52% is the average score of 7 out of 8 tests
100/100 = 1/8x 100% is the average score of 1 out of 8 tests
0.52(7) + 1(1) = 8x her score is 7/8 the first 7 test scores and 1/8 her final test score
4.64 = 8x this represents the mean IF SHE GOT 100% ON THE LAST TEST
0.58 = x 58% would be her final score if she got 100% on the last test
The answer is NO, she cannot pass with merit. Even if Fiona gets 100% on her final test, her mean score would be 58%, and she needs 60% in order to pass with merit. Hope this helps!
