A population has a mean of $300$ and a standard deviation of $90.$ Suppose a simple random sample of size $125$ is selected and X$$ is used to estimate $\backslash$mu $.$ Use z$-$table.

a$.$ What is the probability that the sample mean will be within $+/-8$ of the population mean $($to $4$ decimals$)?$

b$.$ What is the probability the sample mean will be within $+/-12$ of the population mean $($to $4$ decimals$)?$