Given that on one section of the sat the mean is 500 and the standard deviation is 100, what is the approximate probability of a student scoring 400 or lower or 500 or higher on the test?

We are to find for the probability when X≤400 or X≥500

We use the z score formula: z = (x – u) / s

when X≤400, the z is:

z = (400 – 500) / 100 = - 1

when X≥500, the z is:

z = (500 – 500) / 100 = 0

SO from the standard probability tables, the probability at:

P (z ≤ -1 or z ≥ 0) = 0.6587

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50