If you earn 86% on the test with an average of 84% and standard deviation of 4% where the scores are approximately normally distributed what is your percentile

Answer 1

If you assume the test scores are normally distributed, then you can complete this calculation using a traditional Z-Score approach.

Let's summarize the variables:

μ = 84% (0.84)

σ = 4% (0.04)

X = 86% (0.86)

Z = (X-μ)/σ = (0.86-0.84)/0.04 = .50

Z = .50 ... Using a standard z-table, you would find that your area under the curve between your μ and X is 0.1915. Remember, you need to include the values leading up to your mean as well (50%, or 0.50).

The a who scores an 86% would be scoring higher than 0.500 + 0.1915 = 69.15% of their classmates.