A variable is normally distributed with mean $6$ and standard deviation $3.$

a$.$ Determine the quartiles of the variable.

b$.$ Obtain and interpret the $90$th percentile.

c$.$ Find the value that $65\%$ of all possible values of the variable exceed.

d$.$ Find the two values that divide the area under the corresponding normal curve into a middle area of $0\mathrm{.}95$ and two outside areas of $0\mathrm{.}025.$ Interpret the answer.