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Consider $\theta \sim N(\mu,\sigma^2)$. And let $\Phi(\cdot)$ denote the CDF of standard normal distribution.

Then what is the distribution of $\Phi(\theta)$?

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a little suggestion:

$\theta \sim N(\mu,\sigma^2)$ means $\frac{\theta - \mu}{\sigma} \sim N(0,1)$.

You also know that $\Phi(x) = \frac{1}{\sqrt 2 \pi} \int_{- \infty}^x (e^{-x^2/2} dx)$, where $x \sim N(0,1)$

You can try to go on from here

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