Positive random number generation with given mean and standard deviation

I am working on a simulation project. Need help on random number generation. I need two sets of random numbers.

Properties:

1. Primary set (var_a) > Normally distributed, greater than 0, with given mean and std.
2. Secondary set (var_b) -> Same as a primary set, with an addition, that second set cannot be greater than primary set. The reason being the output of a deterministic function will be in percentage between 0-1 only. For example:

service level calculation