Question

Suppose that z~ N(0,1).
a) Find the prob that z < -1.96
b) Find the prob that z => 1.96
c) Find theprob that 0 < z < 1.645

Answer 1

N(0,1) means that z follows the normal distribution, with parameters standard deviation 1 and mean 0.
The table of normal distribution is available at many sources, such as your calculator, or the following link:
http://www.math.unb.ca/~knight/utility/NormTble.htm

Since the area under a probability distribution equals 1.0 and the distribution is symmetrical about the mean, only half of the table (betwen z=0 to infinity) needs to be tabulated. To look for the probability of a negative z-value, you can look up the positive value and subtract from 1.0.
Example
P(-0.5)=1-P(0.5)=1-0.6915=0.3085