# Is it possible to convert calculate the percentile and t-scores from mean and standard deviation?

I need to produce a table that will allow you to look up various types of scores for a test using the number of correct answers like this:

|Raw score|Sten score|z-Score|t-Score|Percentile|
|---------|----------|-------|-------|----------|
|45       |9         |1.701  |?      |?         |
|44       |9         |1.580  |?      |?         |
|43       |8         |1.461  |?      |?         |


I have managed to do it for sten scores and z-scores, but I can't work out how to do it for percentiles and t-scores.

I know that my data is normally distributed, and I know the min/max scores, the mean, the standard deviation, and the sample size... I think it should be possible using this information to calculate the t-scores and percentile, but all the advice I have seen thus far is to just look it up in a table.

If anyone could give me a formula to calculate the t-scores and percentile that would be awesome!