Sheldon Ross Normal Variable

Question

In the below question my query is for (a) part

When we are calculating $P\left \{ \frac{-1}{3}< Z< \frac{2}{3} \right \}$

I know that the normal variable X is converted to standard normal variable and then we look for values in normal table

but I want to know how the third step came?

Please explain anyone.

Comments

P(a$\leq$ X$\leq$b ) ?

z= $\frac{X- \mu }{\sigma }$ 

P(z₁$\leq$z $\leq$z₂) = f(z₂) - f(z₁)

Answer 1

Ayush, the 3rd step is easy to be see. since the z curve is symmetric about z=0, phi(-1/3) = P(z<-1/3) = P(z>1/3) and thus = 1-P(z<1/3)

PS: phi(x) means P(z<x)