How do you find area under a curve between two z values?

Let z1 be the smaller z value and z2 be the larger value. Let N(z) be the cumulative normal distribution evaluated at some value z. The random variable is Z.

The probability that Z has a value from minus infinity to z2 is equal to N(z2). You can show this by drawing a bell shape curve, and shading in everything to the left of z2 as equal to the area under curve.

Similarly, the probability that Z has a value from minus infinity to z1 is N(z1).

The area under the bell curve (standard normal cumulative distribution) is N(z1) - N(z2). I can show this with a little example:

z1= -1 z2 = 2 Area = N(2) - N(-1) = 0.9773 - 0.1587 = 0.8186. I used Excel with the normsdist(z) function. The mean is zero and standard deviation is one with this function.