Question

A set of test scores is normally distributed. If 80% of the scores are above 90 and 30% of the test scores are below 70%, what are the mean and standard deviation of the distribution?

Answer 1

Let shows the population mean and shows the population standard deviation.

Here we need z-score that has 0.20 area to its left and 0.80 area to its right. Using excel function, "=NORMSINV(0.2)" the z-score -0.84 has 0.20 area to its left. So

...............(i)

Now we need z-score that has 0.30 area to its left and 0.70 area to its right. Using excel function, "=NORMSINV(0.3)" the z-score -0.52 has 0.30 area to its left. So

...............(ii)

Subtracting equation (i) from (ii) gives

Standard deviation cannot be negative. It is not possible for normal distribution that 20% observations are less than 90 and 30% less than 70.

So for given statement it is not possible to find mean and SD.