Question

In a normal distribution 10% of the items are under 50 and 90% of the items are the under 80.find the values mean and standard deviation of the distribution?

Answer 1

Given

$$P(Z<z_1)=0.1, z_1= \dfrac{x_1-\mu}{\sigma}=\dfrac{50-\mu}{\sigma}$$

$$P(Z<z_2)=0.9, z_2= \dfrac{x_1-\mu}{\sigma}=\dfrac{80-\mu}{\sigma}$$

$$z_1\approx-1.28155, z_2\approx1.28155$$

$$50-\mu=-1.28155\sigma$$

$$80-\mu=1.28155\sigma$$

$$130-2\mu=0=>\mu=65$$

$$\sigma=\dfrac{80-65}{1.28155}\approx11.7046$$