# Getting the probability of a sample being between two values

I am learning on probabilities in populations and samples now but I'm stuck on this question.

Suppose we have a sample with n=35 of a population with a mean of 80 and standard deviation of 5.

What's the chance of the sample mean being between 79 and 82.

The only formula I got to solve this is this:

In which gekend means that it is known and niet gekend unknown. So I suppose I should use the formula in the second row first column. Which I can't because I don't know S2.

I have searched everywhere but I can't figure it out maybe I am wording it wrong while searching for it.

I think you should use the formula in the first row first column, $\sigma^2$ is known in this case (the square of the population standard deviation, e.g. $\sigma^2=25$). By using the given formula and a probability density table you can calculate $P(79 \leq \bar{X} \leq 82)$...
• I looked up a tutorial which uses σ/sqrt(n) which gives me 0.8451542547285166 which seems to be the right answer to me, but I can't find a way to get the same answer with that formula. Is it really possible with that? – Sinan Samet May 27 '18 at 18:53
• I finally managed to find it apparently for the standard error I just need to get the square root of σ2/n – Sinan Samet May 27 '18 at 19:06