Find the area under the standard normal curve between z-0 and z=3?

P(x)dx = (1/SQRT(2*PI))e^((-z^2)/2)dz

This is the probability distribution for the standard normal curve. You need to integrated this over z=[0,3] to obtain the answer. This can only be done numerically so you'll have to use a calculator or a lookup table. If it helps, you also know that for a standard normal curve, sigma^2 = 1 and mu = 0. You are looking at the area under the curve for 1/2 of 3 standard deviations (1/2 because you are only looking at the area from 0-3 instead of from -3 to 3).

If you look this up in a standard deviation table, I believe you will find 0.9973 for 3 standard deviations and 1/2 of that is .4987 (a standard deviation table includes the area from -sigma^2 to sigma^2 so you need 1/2). If you look it up in a "Z-table" you should see "0.4987" as the value for "3.0" (a Z-table gives you the area from 0 to z, where z is what you look up)