How can I use the normal distribution table to find probabilities other than P(z<Z)?

The normal distribution tables show, for a given Z value, the probability that the random variable z takes a value less than Z or P(z<Z). This is also the area under the normal distribution curve up to Z. We'll call this area A. It is important to remember two things about the normal distribution curve: firstly that the total area under it is 1 and secondly that it is symmetrical.So if we were aiming to find P(z>Z) then we first note that this is the area under the curve from Z upwards. As the sum of the area below Z and above Z must be the total area we see that P(z<Z) + P(z>Z) = 1 and so P(z>Z) = 1-A.In dealing with negative values -Z we use the symmetry of the curve to see that the area below -Z must be equal to the area above Z, giving P(z<-Z) = P(z>Z) = 1-A from the above.Using these two facts we can find the solution to others such as P(z>-Z) or P(m<z<M).