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.

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