# Given a normal distribution with u=20 and the standard deviation =2.5, how do you find the value of x that has (a) 25% of the distribution's area to the left and (b) 45% of the distributions area to the right?

##### 1 Answer

Firstly we must look at the z-score formula, which is

now we can add what we got into our formula so far.

now in question **a**

it tells us that

So to solve for

Thus

then we plot into our formula.

then we solve to get

now to go to question **b**

note that in section **b** here they ask for

as our table is using a **CDF** we know the total area underneat the curve is going to equal

Thus we get that

put the value into our formula and we get.

then we solve for