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?
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
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