Question

Suppose x is a normally distributed random variable with μ=46 and σ=3. Find a value x0 of the random variable x that satisfies the following equations or statements.

a.​ 10% of the values of x are less than x0.

b.​ 80% of the values of x are less than x0.

c.​ 1% of the values of x are greater than x0.

Answer 1

a. $P(Z<z_0)=0.1.$

$z_0=-1.28.$

$\frac{x_0-46}{3}=-1.28.$

$x_0=46-1.28*3=42.16.$

b. $P(Z<z_0)=0.8.$

$z_0=0.84.$

$\frac{x_0-46}{3}=0.84.$

$x_0=46+0.84*3=48.52.$

c. $P(Z>z_0)=0.01\to P(Z<z_0)=0.99.$

$z_0=2.33.$

$\frac{x_0-46}{3}=2.33.$

$x_0=46+2.33*3=52.99.$