Hllo Sai

First of all 96.7 is quite good percentile and yes it can land you up in various Nit's.

You can calculate the predicted rank using the below formula but you cannot calculate the score using the percentile.

((100-percentile)*875000)/100

If you consider the recent trends then yes in this percentile you will get NIt's but most of them will be lower ranked nit's ( Considering good branches). 

You can follow this link for more info : https://engineering.careers360.com/articles/jee-main-cutoff

https://engineering.careers360.com/articles/how-calculate-jee-main-2019-rank-based-on-nta-percentile-score

But if you take my suggestion then please work hard for the 2nd phase exam and try to improve your percentile to much extent so that you can get NITW or NITT or even Surathkal.