Question

. Find the value of Z if the normal curve area between 0 and Z (positive) is 0.4332.

Answer 1

Solve: Normal curve area between 0 and Z is equal to $\int_0^Z$ $\frac{1}{\sqrt{2\pi}}e^\frac{-x^2}{2}dx=\Phi(Z)-\Phi(0)=\Phi(Z),$ where $\Phi$ is Laplas function.

We have: $\int_0^Z \frac{1}{\sqrt{2\pi}}e^\frac{-x^2}{2}dx$ $= 0.4332=\Phi(Z)$. Using the table of values of Laplas function we get: Z = 1.5

Answer: Z=1.5