Question

Consider a normal distribution curve where 90-th percentile is at 20 and the 25-th percentile is at 10. use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

Answer 1

The 25th percentile corresponds to z ≈ -0.67.
The 90th percentile corresponds to z ≈ 1.28.
So, you can write two equations in μ and σ as here:
.. μ -0.67σ = 10
.. μ +1.28σ = 20

The solution is
.. μ ≈ 13.45
.. σ ≈ 5.11