How do you calculate what percentage your score was given me

How do you calculate what percentage your score was given mean, standard deviation, and your score WITHOUT a Z table?

A formula would be very much appreciated! I know it involves an integral, but I do not know how to solve it...

Solution

To answer this question, we take an example: What percentage (or number) of students scored higher than Sarah and what percentage (or number) of students scored lower than Sarah? First, let\'s reiterate that Sarah scored 70 out of 100, the mean score was 60, and the standard deviation was 15 .