Question

How does one look up the z table

Answer 1

First use of the standard z table is used for obtaining probability value (p-value) for z scores.

Lets have an example : we have to find cumulative probability for z till 2.00 i.e. p(z≤2) =?

we will go through vertical column of z till 2.0 and on horizontal row look for 0.00, the intersection value of these column and row will be corresponding p value.

p(z≤2) = 0.97725

Another example: find probability for p(z≤0.14)

we will go through vertical coulmn of z till 0.1 and horizontal row look for 0.04, the the intersection value of these column and row will be corresponding p value.

p(z≤0.14)= 0.55567

- Now if we have negative values of z:

find the p value for z ≤ -1.5 i.e. p(z≤-1.5)

Then we will the concept of symmetry of normal distribution

p(z ≤ -1.5) = p(z ≥ 1.5)= 1- p(z ≤ 1.5)

p(z ≤ -1.5) = 1 - 0.93319

p(z ≤ -1.5) = 0.06681

Second use of Standard z table is to find out z value from corresponding p value.

Example:

1. find cut off z value for p = 0.90

find nearest value of p to 0.90 in table. we have got 0.89973 in table which corresponds to z=1.28

that means p ( z ≤ 1.28) = 0.90

2.

find cut off z value for p = 0.67

find nearest value of p to 0.67 in table. we have got 0.67003 in table which corresponds to z=0.44

that means p ( z ≤ 0.44) = 0.67

Now what if we have to find z value for p=0.33

Since this is a cumulative z table we can not directly find z value for p=0.33

we can do it like below:

0.33 = 1 - 0.67

0.33 = 1 - p ( z ≤ 0.44)

the right hand side of above equation is equal to p ( z ≤ - 0.44)

i.e. 0.33 = 1 - p ( z ≤ 0.44) = p ( z ≤ - 0.44)

hence z value for p = 0.33 is -.0.44

p ( z ≤ - 0.44) =0.33

I hope I have made it clear. If any doubt ask in comments.