# How to use standard normal distribution tables?

What are the important rules to remember when solving problems involving looking up values in a standard normal distribution table?

Specifically,

• When finding the probability using the table, when should I use the $z$ to find a value and when should I use the probabilities to find a value?
• Sometimes when I have this ($z\le 0.6$) they say that I should look for the value by using $z$ and sometimes by searching for the nearest two probabilities and which $z$ they are, add them and divide them by 2. So I would like to know when to use each one?
• $z$-values are in the margins. Probabilities are within the table. To remember this, note that the margins contain values that are negative or larger than one; therefore they cannot be probabilities. Jun 3, 2013 at 4:56
• I've seen tables organized at least four different ways. What tables are you using? Jun 3, 2013 at 5:46
• @Glen_b I am using Cumulative normal distribution ( z table) Jun 3, 2013 at 6:19
• So if I look up $-2.4$ it has an entry? If I look up $0$ what probability does it give? Jun 3, 2013 at 6:23
• @ocram Thank you :) , But the z-values starts from 0.0 . Now if they asked me to find the probability that means I use z to find it . and if they asked to find the nth percentile that means I use the probability to find the z values , add them and divide them by 2 . right? Jun 3, 2013 at 6:28

When finding the probability using the table, when should I use the z to find a value

when you have a $z$ and need a probability.

and when should I use the probabilities to find a value?

when you have a probability and need a $z$.

Sometimes when I have this ($z≤0.6$) they say that I should look for the value by using $z$ and sometimes by searching for the nearest two probabilities and which $z$ they are, add them and divide them by 2. So I would like to know when to use each one?

If your probability value is in the body of the table/$z$-value in the margins (or really close to a value), you can use the probability.

If your probability(/$z$ value) is in between, the corresponding $z$ (/probabilities) are in between. The usual thing is to do linear interpolation, but it sounds from your description like they're just asking you to take the midpoint of the two probabilities either side.

[There's some explicit examples of using the tables here and here.]

Here is a simple, layman explanation. The first thing you would need is the z score given by

Z score = ( x – µ ) / σ

Once you have the Z score, you interpolate the same

For example lets say we get a Z Score of 0.32. Since this is a positive z score, we will be using positive side of the standard normal distribution table(table 1.2)

Now first find the corresponding value for the first two digits 0.3 on the y axis. Next repeat the same for 0.02 along the x axis and we get the value as 0.62552

Hope this helps you. Ofcourse the core concepts and how the things works when explained in technical terms is much more complicated.

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