Question

Can someone explain how to use z table? How to convert and use it in Stats?

Answer 1

A Z-Score Table, is a tablethat shows the percentage of values (or area percentage) to the left of a given z-score on a standard normal distribution.

These are the steps to find probability(Area) for the given Z-score:-

1.Go to the row that represents the ones digit and the first digit after the decimal point (the tenths digit) of your z-value.

2.Go to the column that represents the second digit after the decimal point (the hundredths digit) of your z-value.

3.Intersect the row and column from Steps 1 and 2.

This result represents p(Z < z), the probability that the random variable Zis less than the value z (also known as the percentage of z-values that are less than the given z value ).

For example, suppose you want to find P(Z < 2.13). Using the Z-table below, find the row for 2.1 and the column for 0.03. Intersect that row and column to find the probability: 0.9834. Therefore P(Z < 2.13) = 0.9834.

Similarly we can see tha probability of P(Z<-2.13)=0.0166

For P(Z<2.13)=0.9834

We can see it as

2.1(See in left column)+0.03( see in top most row)= 2.13

Hence from the table u will get area of 2.13 on intersection of 2.1 row and 0.05 column is 0.9834.

Aslo we can fine Z - score if probability is given.

P(Z<z)=0.9834

For z we can see table for the prob. 0.9834

Which is equal to 2.13