# Finding the Probability when the variance , sample mean and a different sample size is given

I'm quite confused about how to find the probability when the variance , sample mean and a different sample size is given.

I have found the variance an the sample mean through the MLE (maximum likelihood estimator). And now I have to find the probability of some occurrence of the RV(in a normal distribution) takes when a new sample size is given. Please can someone help with this issue.

If you know (or assume) your distribution is Gaussian with estimated mean $\mu$ and estimated variance $\sigma^2$, then the probability a single draw occurs between $x_l$ and $x_u$ is:
$$P[x_l < x < x_u] = \int\limits_{x=x_l}^{x_u} {1 \over \sqrt{2 \pi} \sigma} e^{-(x-\mu)^2/(2 \sigma^2)}\ dx$$,