If Jill's mark is in the 20th percentile, what was her test score?

Question

A class of 26 students has test scores normally distributed with a mean of 54 and a standard deviation of 6.2

Answer 1

Figure out what the z score is for 20th percentile. On my old TI-83 under the DISTR menu I would use invnorm(0.20) for that.*

 

Then this z = (x-μ)/σ; you know all of the values in this equation except x, so solve for that x score, which corresponds to the z score that corresponds to area under the normal curve 0.20.

*My calculator is not available, so you'll have to do this step, which could also be done by reverse table lookup, e.g. finding the z for probability 0.2000