Question

using the table, give the percentage associated with each unit of standard deviation in the standard normal curve to the nearest hundredth.

x	area, a(x)	x	area, a(x)
0.4	0.1554	2.4	0.4918
0.6	0.2257	2.6	0.4953
0.8	0.2881	2.8	0.4974
1.0	0.3413	3.0	0.4987
1.2	0.3849	3.2	0.4993
1.4	0.4192	3.4	0.4997
1.6	0.4452	3.6	0.4998
1.8	0.4641	3.8	0.4999
2.0	0.4772	4.0	0.5000
standard deviation	percentage area

| 2.4 | %
| 1.6 | %
| 0.4 | %
| 1.4 | %
| 3.6 | %

Explanation:

Step1: Locate value in table

Find the given standard - deviation values in the left - hand column (x) of the provided table.

Step2: Read corresponding area

Read the corresponding area value (A(x)) from the right - hand column for each x value.

Step3: Convert to percentage

Multiply the area value by 100 to get the percentage.

For a standard deviation of 2.4:
The area from the table is 0.4918.
Percentage = 0.4918×100 = 49.18%

For a standard deviation of 1.6:
The area from the table is 0.4452.
Percentage = 0.4452×100 = 44.52%

For a standard deviation of 0.4:
The area from the table is 0.1554.
Percentage = 0.1554×100 = 15.54%

For a standard deviation of 1.4:
The area from the table is 0.4192.
Percentage = 0.4192×100 = 41.92%

For a standard deviation of 3.6:
The area from the table is 0.4998.
Percentage = 0.4998×100 = 49.98%

Answer:

Standard Deviation	Percentage Area
1.6	44.52%
0.4	15.54%
1.4	41.92%
3.6	49.98%