how to create a variable with conditional distribution

Hi, dear friends,

May I ask for help for the following code:

I want to create a random number X,

1. original X (unconditional X) follows a normal distribution with mean = 12.21 and SD=0.63.
2. given Y=11.50, the probability (X>=Y)>=0.97.

I think this is not a simple truncated normal distribution because the probability (X>=Y) is not 100%.

Can any one give me some help?

I really appreciate

Best,

Yanting