Let $X\sim \mathcal N(\mu,\sigma^2)$. Given a simple random sample I know that $$\left[\bar X - z_{1- \alpha/2} \frac{\sigma}{\sqrt{n}},\bar X + z_{1- \alpha/2} \frac{\sigma}{\sqrt{n}}\right]$$ is a $1-\alpha$ confidence interval for $\mu$.
What will be the new confidence interval for $\tau(\mu)=\dfrac{e^\mu}{1+e^\mu}$?