finding percentile


can someone help me set this up to solve. i know i had missed this on one my previous exam, and trying to study for tomorrow final exam.

scores on a test are normally distributed with a mean of 65.3 and a standard deviation of 10.3. find p 81 (percentile 81) which separates the bottom 81% from the top 19%,

the answer is 74.4

how do i sovle for the percentile.


Dark Knight
Let X follows N (mean=65.3 and sd 10.3).

Now you have to calculate K such that P(X <K )=.81

Convert into Standard Normal
P[ (X-mean)/sd < (K-mean)/sd] =.81
P[Z <(K-mean)/sd] =.81

Now from normal table calculate Za such that P[Z<Za]=.81

then solve K.
First find Znormal value that corresponds to area from -infinity to +Z as 0.81 (given).
Now this value of Z = (X-Mean)/ standard deviation.Since mean & s.d. are known you can find X which is unknown.