Based on my knowledge the quantiles are from 0.0 to 1.0 for a continuous variable. JMP shows that nicely on the distribution platform. But when I save the Normal Quantiles to a table, I also see negative quantile values and more than 1.0 values. Which does not make sense? How do I interpret these values and convert them to quantiles in the range from 0.0, 0.25, 0.50, 0.75 and 1.0.
The values of 0 to 1 are the probabilities. The quantiles are the values of your variable that correspond to a given portion or probability of the distribution. So the 10% means that Pr( X < quantile ) = 0.1 in such a case.
I interpreted your question differently than Mark Bailey did. Just in case your question is the way I took it:
When you are in the Distribution report and choose Save > Normal Quantiles from the red triangle, the column that is added is the value for a normal quantile for that row.
For example, suppose you had a small dataset with values 2, 4, 6, and 8. The value of 2 would be a quantile of .20 (20% of the distribution is less than this value). What point is that on a normal curve? That would be -0.84. 20% of the normal distribution is less than -0.84. These are the values that are saved in the column. Therefore, your values in this column will typically be between -3 and +3, but it is possible to see values outside of that range.