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I just took an online test and I was notified that the average score for the test was 45% (out of 100%) and I received a 72%.

Using these 2 pieces of information would it be possible to calculate under what percentile I fall for test scores?

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No, that would not be possible without further information about the distribution.
Consider for example a situation where there were only 2 students, you got 72 and the other person got 18. In that case you did the best. Consider another alternative where two people got 0, you got 72, and 2 people got 73. In that case, you were right in the middle of the pack.

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This is clearly impossible. To appreciate this just consider two possible scenarios of 100 people having taken the test so far.

  • 100 scored 45%
  • 45 scored 100%, 55 scored 0%

In the first case you are the best, in the second a bit above average.

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