
probability
The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value $\displaystyle 10 $ min and a standard deviation $\displaystyle 2 $ min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most $\displaystyle 11 $ minutes?
So is this just $\displaystyle P \left(z \leq \frac{1}{2/\sqrt{5}} \right) = \Phi(1.118) = 0.8686 $ and $\displaystyle P \left(z \leq \frac{1}{2/\sqrt{6}} \right) = \Phi(0.816) = 0.7939 $?

I get 0.8682 for the first one.
On the second you have the wrong value for $\displaystyle \frac{\sqrt{6}}{2}$