Let $\displaystyle X_1,...,X_{25}$ be from a sample of 25 from a normal distribution $\displaystyle N(\theta,100)$. Find a UMP region with $\displaystyle \alpha = 0.1$ for testing $\displaystyle H_0:\theta=75 \ VS \ H_1:\theta>75$

So after performing the Likelihood ratio test, I determined the critial region to be $\displaystyle (\Sigma X_i => K)$ where K is some constant.

Using the CLT $\displaystyle \frac{\Sigma X_i - n\mu}{\sigma \sqrt{n}}$

$\displaystyle P(\Sigma X_i => K) =P_{H_0}( \frac{\Sigma X_i - 25(75)}{10\sqrt{75}} => \frac{K - 25(75)}{10\sqrt{75}} )=0.1$

$\displaystyle \frac{K - 1875}{86.6}=1.28$ solving for K = 1985.848

Have I made a mistake anywhere?