Chapter 6.3, Problem 2E

Solution

To provide: The procedure to find the given probability using standard normal table.

Given information: 

  $P\left(z\le 1.4\right)$

Explanation:

To determine the corresponding probability (area under the curve) for a z score:

1. Go to the row that has z score's first two digits, that is, 1.4.
2. Cross over to the column that has z score as the third digit, that is 0.00.
3. Find the value at the point where the preceding steps' row and column overlap.

The table is:

Z	0	0.01	0.02	0.03
0	0.5	0.504	0.508	0.512
0.1	0.5398	0.5438	0.5478	0.5517
0.2	0.5793	0.5832	0.5871	0.591
0.3	0.6179	0.6217	0.6255	0.6293
0.4	0.6554	0.6591	0.6628	0.6664
0.5	0.6915	0.695	0.6985	0.7019
0.6	0.7257	0.7291	0.7324	0.7357
0.7	0.758	0.7611	0.7642	0.7673
0.8	0.7881	0.791	0.7939	0.7967
0.9	0.8159	0.8186	0.8212	0.8238
1	0.8413	0.8438	0.8461	0.8485
1.1	0.8643	0.8665	0.8686	0.8708
1.2	0.8849	0.8869	0.8888	0.8907
1.3	0.9032	0.9049	0.9066	0.9082
1.4	0.9192	0.9207	0.9222	0.9236
1.5	0.9332	0.9345	0.9357	0.937

The required probability is 0.9192.