Get help with upper level probability

Assuming the null hypothesis is true, what is the probability that our z-test statistic would fall outside the z-critical boundaries (in the tails of the distribution the region of rejection) for anв $\alpha =0.05?$

$\frac{8!}{(5!\times 3!)}$

The area between $z=0$ and $z=1.1$ under the standard nomad curve is ?

Find the probability density function of $Y=e^X$, when X is normally distributed with parameters $\mu \text{and}{\sigma }^2$. The random variable Y is said to have a lognormal distribution (since log Y has a normal distribution) with parameters $\mu \text{and}{\sigma }^2$

A population of values has a normal distribution with ${\displaystyle \mu =198.8}$ and ${\displaystyle \sigma =69.2}$. You intend to draw a random sample of size ${\displaystyle n=147}$.
Find the probability that a sample of size ${\displaystyle n=147}$ is randomly selected with a mean between 184 and 205.1.
${\displaystyle P\left(184<M<205.1\right)=}$?
Write your answers as numbers accurate to 4 decimal places.