A problem asks that based on sample of size n from a Normal($\theta$,$1$) distribution, we find the Uniformly Minimum Variance Unbiased Estimator (UMVUE) for: $$p=\Phi(x-\theta)$$
Where $\Phi$ is the CDF of the normal distribution.
My problem is understanding how can I find an estimator for something that is not a parameter of the distribution?
I have tried guessing an estimator and improving it, but again, get stuck with estmating a function instead of a parameter.