There are two separate aspects to this question. The first is the mechanics (or formula) to make the conversion and the second is the definition(s) of normal or standard conditions.
Regarding the formula to use - breizh has given the correct answer. Note that the way breizh has put this formula is basically to say that mass (or molar) flow is constant. This is a good way to remember the formula because people sometimes have problems to remember which conditions go above and below the line if it is just expressed as V2 = (P1 x V1 x T2) / (P2 x T1). This procedure of converting volumetric flow to mass flow and then to the new volumetric conditions is the way it is handled in Uconeer.
The situation regarding the definitions of normal and standard conditions is much less clear. As I have often written here, there is nothing normal or standard about normal and standard conditions.
There are so many standard conditions that nothing is standard anymore. The use of standard conditions is in contractual transfer of gas, and in those cases the standard is defined in each contract. In Europe standard conditions are relatively standard at 15°C and 101.325 kPa (= 1 atmosphere). But even this is not certain and the standard conditions should be included with every document or calculation. In the USA the situation is totally chaotic, and each organization has their own definition.
When I (and PK Rao) were young engineers the definition of normal conditions was something that could be fairly well relied on because it was defined by IUPAC as 0°C and 101.325 kPa. Unfortunately IUPAC changed their definition quite a while back and it is now 0°C and 100.000 kPa. Many old texts (and old engineers) still use the 101.325 kPa definition so it is as important for normal conditions as for standard that the conditions are defined every time. Just as an example of how confusing the situation is, PK Rao has mixed up the two definitions in post #9 because 760 mmHg is not the same thing as 1 bar. He is correct that the 1 bar ( = 100.000 kPa) is the new definition, but it was never defined (by IUPAC) as 760 mmHg (which is very close to 1 atmosphere).
There used to be a very good summary of all of this on Wikipedia, but at the moment it claims that the old and new IUPAC definitions are both at 101.325 kPa.
With all this confusion surrounding the subject the comment by gegio1960 is totally out of line and of no help to anybody and I suggest that he deletes it.