A set of examinations marks is approximately normally distributed with mean of $75$ and standard deviation of $5$. If the top $5\%$ of the students gets Grade A and bottom $25\%$ of gets grade F. What is the lowest mark in grade A, the highest mark in grade F?
Bottom $25\%$
$X=(-0.5948)\times5+75 $ #Z value of $0.25$ is $-0.5948$
$=72.00$ ( I got the answer as $72$)
Top $5\%$
$X=(Z)\times5+75$
$=0.829*5+75$ # Z value of $0.95$ is $0.8289$
$=79$
I should get answer as $72$ & $83$ (thats how its in my text book) but I'm not getting the correct answer for the top $5\%$. Did I apply the right procedure?