Z table transformation

We will use below table to calculate our probability.

                                                             Fig 1:

Lets solve some of the below problems to get more idea on transformation.

What is the probability of P(z<=1.5)

We need to find out the below highlighted area.

To find the answer using the Z-table(see the Fig 1:), find where the row for 1.5 intersects with the column for 0.00; this value is 0.9332.

Note: P(z<=1.5) = P(z<1.5)

What is the probability of P(z>=1.5)

We need to find out the below highlighted  area.

The area under the curve or total probability of normal distribution  is 1 means 100%, so

P(z>1.5)+P(z<1.5) = 1

P(z>1.5) = 1 – P(z<1.5) = 1-0.9332=0.0668 (We already calculated P(z<1.5))

What is the probability for P(z<=1.67)

To find the answer using the Z-table(see the Fig 1:), find where the row for 1.6 intersects with the column for 0.07; this value is 0.9525.