Question 968685
Using the standard normal distribution chart, find the probabilities in the following problems.
<pre>
Go to this site to find a standard normal distribution chart:

https://www.easycalculation.com/statistics/normal-ztable.php

The table on that page gives area between z=0 and whatever z-score you have.
</pre>
P(0 < z < 1.68)
<pre>
Find 1.6 in the left-most column on that page headed z.
Go across to the next to last column headed 0.08 and read 0.4545

That's the answer: 0.4545
</pre>
P(z > 1.39)
<pre>
Find 1.3 in the left-most column on that page headed z.
Go across to the very last column headed 0.09 and read 0.4177
But that's not the answer. That's the area between z=0 and z=1.39.
The entire area to the right of z=0 is 0.5, so to find the area
to the right of 1.39, we subtract 0.4177 from 0.5:

 0.5000
-0.4177
-------
 0.0823
</pre>
P(-1.65 < z < 2.47)
<pre>
You must do that in two parts:

P(-1.65 < z < 0)  and P(0 < z < 2.47) and add them together.

First part: P(-1.65 < z < 0)
By  symmetry, P(-1.65 < z < 0) is the same as P(0 < z < 1.65)

Find 1.6 in the left-most column on that page headed z.
Go across to the column headed 0.05 and read 0.4505
But that's only the left part of the answer, the area between 
z=-1.65 and z=0.

Second part: P(0 < z < 2.47)

Find 2.4 in the left-most column on that page headed z.
Go across to the column headed 0.07 and read 0.4932
That's the left right part of the answer, the area between 
z=0 and z=2.47.  We must add those together:

 0.4505
+0.4932
-------
 0.9437
</pre>
P(z < 2.23)
<pre>
Find 2.2 in the left-most column on that page headed z.
Go across to the column headed 0.03 and read 0.4871
But that's not the answer. That's the area between z=0 and z=2.23.
The entire area to the left of z=0 is 0.5, so to find the entire
area to the left of 2.23, we must add 0.5 to 0.4871:

 0.4871
+0.5000
-------
 0.9871

Edwin</pre>