hello world! this is my first post to this forum.

please answer to the following seemingly classical probability question, it's urgent for me:

suppose X is a Poisson(1) random variable, and Z is a Standard Normal {N(0,1)} random variable. what is the result of the following probability:

P(X > (16 - Z^4) / (X + Z^2)) < 3/8

PS. by the sign ^ i mean power, so e.g. Z^4 is Z to the power of four.