How do you calculate the standard normal random variable?

The questions I have starts with the following information:





Let Z be a standard normal random variable.





a) Find P (Z %26gt; 2)





b) Find Z such that P (z %26lt; Z) = 0.999





c) Find P (|Z| %26lt; 1.96)





d) Find P (|Z| %26gt; 1.96)





e) Find P (Z %26gt; 1.96)





f) Find P (Z %26gt; -1.96)





These questions were given on a mock examination paper, and the information above was all that was provided. Any help would be greatly appreciated!

How do you calculate the standard normal random variable?
You need to use the normal distribution tables for this.





Usually the probabilities in the table refer to z %26lt; 2





The probability of z %26gt; 2 is 1 - P(z%26lt;2).