Applying antiderivatives to normally distributed sets of data (bell curve/z scores)
Me and my G12 teacher are having a debate about a question he marked wrong on one of my tests.
The question was true or false:
I put false, reason being it truly isn't undefined. Z scores can continue on to positive/negative infinity, all of which are defined. Z scores > 4 perhaps are negligable, but most definitely not undefined.
Z scores > 4 are undefined. T/F?
The reason my teacher says it is undefined is because of the way we go about calculating the probability using the z scores. Instead of using the antiderivative (the accurate way to determine percentages from a z score, i would think), we use a table that has z scores and their corrosponding percentages listed. We simply round to the nearest percent.
Since the table we use only goes to a min of -4 and a max of +4, he says that all scores above and below that range are undefined.
The class im taking is a financial math class, which is why we use a simple table rather than figuring out the antiderivative of the normal distribution curve. I hope to show my teacher that the way the table he uses was generated was using calculus, and more importantly z scores above and below -4/+4 are most definitely not undefined.
The problem I've encountered, is I'm a bit rusty since my calculus classes a few years ago, and I can't find the equation of normally distributed data :\.
Through a bit of searching, I found that the normal distribution is a form of the gaussian function.
I got the equation , but the problem is the total area under the curve doesn't come to 1, how can i mold it so it does come to 1, so that when I find the area under a certain section of the curve it will be a percent in decimal form?
any help would be appriciated,