A group received test scores with a mean of 80 and a standard deviation of 10. How do I calculate what percentile 90 and 60 are in?

Question

Would 90 fall within the top 10% of scores? And does 60 fall within the bottom 10% of scores?

Answer 1

We need to calculate a z-score for each value:

z = (x - μ)/σ

where:

μ = 80

σ = 10

For x = 90:

z =(90 - 80)/10 = 1

Using a z-score table, we obtain the value 0.8413 or 84.13% which means that 1 - 0.8413 = 0.1587 or 15.87% of people scored above a 90.

For x = 60:

z = (60 - 80)/10 = -2

Using a z-score table, we obtain the value 0.0228 or 2.28% which means that 2.28% of people scored below a 60.