The normal probability plot is used as a tool to examine the normality of a distributiuon. Frequently it is used to ascertain whether a particualar statistical technique (that assumes normality) can be applied to the data reliably.

To obtain a normal probability plot, first put your values in ascending order.

Where the numbers in brackets represent the order of the value.

Using the order number (i) find the normal score by 'solving'...

...for z(i).

The i/(n+1) bit gives the cumulative quartiles.

So you calculate i/(n+1) then look it up on the normal table (or generate them using a computer) for example if i/(n+1)=0.938220 then z(i)=1.54.

You then plot z(i) vs x(i) to get the probability plot vs the standard normal distribution.

If the plot is pretty much a straight line, you can be confident that your data is normally distributed around an average value.

The above plot indicates a heavier tailed plot than the normal distribution. I used a t-distributed data set with a d.f value of 4.

This probability plot indicates a right skew on the data which is otherwise normally distributed. Here there are more higher and lower values than would be expected if this were a normally distributed data set.

Generally speaking the larger the data set the more reliable the plots. Sample sizes less than 30 or would potentially show large deviations from normal even if they are normal data sets.

Looks a bit squiffy, but that's because it's a small sample.