Calculating probability of an individual score

A

altitus

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The question I am working on is: Given that the mean is 500 and the standard deviation is 100 on one section of the SAT, what is the approximate probability of a student scoring 400 or lower on the test?

a. .84
b. .50
c. .16
d. .34

I have another question that is almost exactly the same as this one, except it asks for the probability of a student scoring 400 or higher on the test. My text explains that first, you have to find the x score of the problem, which I determined was -1. The text uses a problem similar to this one to demonstrate the concept. It reads: "In order to determine the probability of selecting a student with an intelligence test score this high or higher, we take the area between the mean and the z score."

This area is .34134 for a z score of -1. Then you have to add .50 from the other half of the distribution to it. Therefore, the answer is that the probability is .84134, or approximately 84%.

So I determined that this was the answer, but the problem I'm trying to solve now is asking for the same work, but this time for the probability of someone scoring 400 or lower instead of 400 or higher on the SAT section. I'm not sure how the answer is supposed to differ, or how to explain why.
 
Draw a bell curve. Place 500 in the middle and 400 to the left.

How much is the entire area from the extreme left to the extreme right? For a moment call this number k.

Now you claim that the area above 400 is .84134. So what is the area below 400? Just think about it, the area below 400 and the area above 400 is all the area which totals to k. So how do you find the area below 400? The final answer should use the correct value for k.

For the record do you think that given any score the same number of students get below that number as that get above that number? On a class exam (from any one of your classes) that follows a bell curve you really think that if 5% of the students got below a grade of 25 (a very poor grade) then 5% of the students got a score above 25? That only accounts for 50% (helpers let this go) of the students! What happened to the rest of the students?
 
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