Question 848064
a) P[-2.03<Z<1.23]

Think about what this means. We want all the area left of 1.23, but we want to take away the area left of -2.03.

P[Z<1.23] - P[Z < -2.03]

Notice that the area left of -2.03 is the area right of 2.03, or since the entire area is 1, it's 1 -P[Z<2.03]

So we have:

P[Z<1.23] - (1-P[Z<2.03])

Now we can use the standard normal table. <http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm> Let's call the standard normal lookup function {{{phi}}}. 

{{{phi(1.23) - (1-phi(2.03))}}}

{{{.8907 - (1-.9788) = highlight(0.8695)}}}


2. P[Z>1.63].  As I mentioned before, since the entire area under the curve is 1, then 1- P[Z<1.63] is another way to represent this.

Using {{{phi}}}

{{{1 - phi(1.63)}}} 

{{{1-.9484 = highlight(.0516)}}}