Using the standard normal distribution chart, find the probabilities in the following problems.
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.
P(0 < z < 1.68)
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
P(z > 1.39)
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
P(-1.65 < z < 2.47)
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
P(z < 2.23)
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
