A standard normal distribution has mean 0 and standard deviation of 1; if you want to make a distribution with mean m and deviation s, simply multiply by s and then add m. Since the normal distribution is theoretically infinite, you can’t have a hard cap on your range e.g. (100 to 150) without explicitly rejecting numbers that fall outside of it, but with an appropriate choice of deviation you can be assured that (e.g.) 99% of your numbers will be within the range.
About 99.7% of a population is within +/- 3 standard deviations, so if you pick yours to be about (25/3), it should work well.
So you want something like: (normal * 8.333) + 125