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Table 1. Per Capita Personal Income and Z-score by State for 1997

STATE	INCOME (x)	Z-score of x
Alabama	20,842	-0.9535
Alaska	25,305	0.2471
Arizona	22,364	-0.5440
Arkansas	19,585	-1.2916
California	26,570	0.5874
Colorado	27,051	0.7168
Connecticut	36,263	3.1948
Delaware	29,022	1.2469
Florida	25,255	0.2336
Georgia	24,061	-0.0876
Hawaii	26,034	0.4432
Idaho	20,478	-1.0514
Illinois	28,202	1.0264
Indiana	23,604	-0.2105
Iowa	23,102	-0.3455
Kansas	24,379	-0.0020
Kentucky	20,657	-1.0032
Louisiana	20,680	-0.9970
Maine	22,078	-0.6210
Maryland	28,969	1.2327
Massachusetts	31,524	1.9200
Michigan	25,560	0.3157
Minnesota	26,797	0.6484
Mississippi	18,272	-1.6448
Missouri	24,001	-0.1037
Montana	20,046	-1.1676
Nebraska	23,803	-0.1570
Nevada	26,791	0.6468
New Hampshire	28,047	0.9847
New Jersey	32,654	2.2239
New Mexico	19,587	-1.2911
New York	30,752	1.7123
North Carolina	23,345	-0.2802
North Dakota	20,271	-1.1071
Ohio	24,661	0.0738
Oklahoma	20,556	-1.0304
Oregon	24,393	0.0018
Pennsylvania	26,058	0.4496
Rhode Island	25,760	0.3695
South Carolina	20,755	-0.9769
South Dakota	21,447	-0.7907
Tennessee	23,018	-0.3681
Texas	23,656	-0.1965
Utah	20,432	-1.0637
Vermont	23,401	-0.2651
Virginia .	26,438	0.5519
Washington	26,718	0.6272
West Virginia	18,957	-1.4605
Wisconsin	24,475	0.0238
Wyoming	22,648	-0.4676
m =	24,386	0
s =	3755.1	1.0000

Table 2. Per Capita Personal Income, f(x) and f(z) by State for 1997

STATE INCOME (x) f(x) f(z)

Alabama ............... 20,842 6.8117E-05 0.2532 ChartObject Chart 1

Alaska ................ 25,305 1.0409E-04 0.3869

Arizona ............... 22,364 9.2552E-05 0.3441

Arkansas .............. 19,585 4.6603E-05 0.1732

California ............ 26,570 9.0312E-05 0.3357

Colorado .............. 27,051 8.3005E-05 0.3086

Connecticut ........... 36,263 6.5215E-07 0.0024

Delaware .............. 29,022 4.9320E-05 0.1833

Florida ............... 25,255 1.0443E-04 0.3882

Georgia ............... 24,061 1.0690E-04 0.3974

Hawaii ................ 26,034 9.7277E-05 0.3616

Idaho ................. 20,478 6.1749E-05 0.2296

Illinois .............. 28,202 6.3374E-05 0.2356

Indiana ............... 23,604 1.0496E-04 0.3902

Iowa .................. 23,102 1.0110E-04 0.3758

Kansas ................ 24,379 1.0731E-04 0.3989

Kentucky .............. 20,657 6.4880E-05 0.2412

Louisiana ............. 20,680 6.5283E-05 0.2427 ChartObject Chart 4

Maine ................. 22,078 8.8496E-05 0.3290

Maryland .............. 28,969 5.0199E-05 0.1866

Massachusetts .... 31,524 1.6990E-05 0.0632

Michigan .............. 25,560 1.0210E-04 0.3796

Minnesota ............. 26,797 8.6968E-05 0.3233

Mississippi ........... 18,272 2.7746E-05 0.1031

Missouri .............. 24,001 1.0674E-04 0.3968

Montana ............... 20,046 5.4279E-05 0.2018

Nebraska .............. 23,803 1.0600E-04 0.3941

Nevada ................ 26,791 8.7059E-05 0.3236

New Hampshire .... 28,047 6.6087E-05 0.2457

New Jersey ............ 32,654 9.0503E-06 0.0336

New Mexico ........ .. 19,587 4.6635E-05 0.1734

New York .............. 30,752 2.4773E-05 0.0921

North Carolina ........ 23,345 1.0318E-04 0.3836

North Dakota .......... 20,271 5.8147E-05 0.2162

Ohio .................. 24,661 1.0702E-04 0.3979

Oklahoma .............. 20,556 6.3112E-05 0.2346

Oregon ................ 24,393 1.0731E-04 0.3989

Pennsylvania .......... 26,058 9.6997E-05 0.3606

Rhode Island .......... 25,760 1.0023E-04 0.3726

South Carolina ........ 20,755 6.6595E-05 0.2476

South Dakota .......... 21,447 7.8504E-05 0.2918

Tennessee ............. 23,018 1.0028E-04 0.3728

Texas ................. 23,656 1.0526E-04 0.3913

Utah .................. 20,432 6.0946E-05 0.2266

Vermont ............... 23,401 1.0361E-04 0.3852

Virginia .............. 26,438 9.2157E-05 0.3426

Washington .......... 26,718 8.8155E-05 0.3277

West Virginia ......... 18,957 3.6937E-05 0.1373

Wisconsin ............. 24,475 1.0728E-04 0.3988

Wyoming ............... 22,648 9.6199E-05 0.3576

m = 24,386 0 0

s = 3755.1 2.8920E-05 0.1075

Table 3. Finding Areas Under the Curve of the Z-distribution using Trapezoids

THEORETICAL STATISTICAL FUNCTION, f(Z)

z-scores h1=f(z) h area interval Finding areas:

-3 0.0044 0.5 0.0055 (-2.5 to 3) Use the area of a trapezoid to

-2.5 0.0175 0.5 0.0179 (-2 to -2.5) determine area under the curve

-2 0.0540 0.5 0.0459 (-1.5 to -2) or probabilities for every change

-1.5 0.1295 0.5 0.0929 (-1 to -1.5) in h or .5 increment in z-scores.

-1 0.2420 0.5 0.1485 (-.5 to -1)

-0.5 0.3521 0.5 0.1878 (0 to -.5)

0 0.3989 0.5 0.1878 (0 to .5)

0.5 0.3521 0.5 0.1485 (.5 to 1)

1 0.2420 0.5 0.0929 (1 to 1.5)

1.5 0.1295 0.5 0.0459 (1.5 to 2)

2 0.0540 0.5 0.0179 (2 to 2.5)

2.5 0.0175 0.5 0.0055 (2.5 to 3)

3 0.0044 0.5

Figure 5. Smoothed histogram for the Standard Normal Distribution
ChartObject Chart 1

Table 4. Twenty-five Randomly Selected Samples of Income of Sample Size=20

Sample #1 Sample #2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

25255 31524 19585 23345 19585 28969 26438 25305 23656 24379 20478 25255 18957 23018 32654 36263 23604 23345 24475 27051 23102 26797 28047 24001 23102

22648 25760 20432 24475 29022 19587 19585 30752 19585 20842 36263 26570 26034 24061 23604 24061 20842 26791 26797 20842 23345 20478 24475 23018 22364

23345 22364 20478 18957 24661 26797 21447 23656 20680 28969 26797 22364 24001 23401 20657 28047 28047 28047 23018 24393 26718 28047 25255 23604 25760

23018 30752 20755 28969 20271 20432 20657 23803 30752 24393 29022 24475 28969 32654 24475 19587 22648 24001 20657 25560 26797 24393 18957 28202 23018

18272 24061 20657 25560 36263 26791 26034 23604 28047 20046 20842 25760 26791 24001 25305 19585 28202 26034 28202 24061 20046 19585 22078 23102 20556

23401 23803 24001 20432 27051 32654 29022 19587 23018 29022 20755 26797 22648 23803 19587 20046 26438 24379 26718 25305 23604 26034 25305 22078 20842

23656 20271 28969 23656 20556 24661 20432 27051 20046 19585 23656 26718 24661 36263 24393 25560 25760 20478 26791 20556 20432 28202 21447 22648 24661

25760 20657 23803 27051 26034 22078 23803 20046 27051 26034 19585 29022 18272 28202 28047 20755 19585 18957 23102 25255 22364 26438 20432 20657 26797

20680 23656 24393 20478 20842 18272 26058 24061 20271 23604 22648 31524 23345 30752 21447 31524 28969 23401 20046 23018 24001 26570 24001 32654 20680

25560 20556 19587 22078 22364 20680 24475 25560 23604 20478 20556 20046 24475 26570 23401 18957 27051 31524 30752 20271 28969 25760 18272 29022 18957

20755 20842 23102 23018 28969 23401 23345 20657 24379 23656 30752 20432 27051 23656 20271 23401 23401 25760 25305 26718 23803 24475 25560 26718 23803

31524 21447 24061 23102 22648 26718 22364 20755 24661 25760 18272 24001 22078 23102 20842 20657 22078 26570 36263 23604 30752 26718 23803 20842 28202

29022 24475 23018 28202 26797 25255 19587 20432 21447 32654 22364 22078 26058 29022 20432 24379 24001 25560 18957 30752 24061 24661 26034 28047 26570

20842 20755 25255 26034 32654 22364 23102 23102 22648 20657 27051 24661 24379 23345 20755 20432 32654 28969 31524 23656 26058 32654 20680 26791 23656

22078 26438 28047 24661 22078 30752 18272 29022 24475 19587 26438 20680 24393 20432 26438 26570 20680 27051 24379 24001 23656 23345 26570 23656 29022

18957 26058 30752 20755 31524 26058 20680 22078 23345 28202 22078 25560 25305 28969 30752 23102 24661 24061 20271 19587 28047 23401 19585 30752 25255

24475 18272 26034 22364 24379 26034 36263 25760 18272 20755 20657 23345 21447 24661 23102 32654 23018 20271 19587 29022 25760 30752 20842 31524 28969

19587 24379 21447 26718 18272 23656 20046 26718 25255 25255 19587 23401 22364 25560 36263 30752 26718 20046 26034 20046 25255 24379 19587 20478 24475

24393 26718 31524 23401 30752 20046 31524 24379 20657 30752 23345 20478 28047 26438 23803 24393 25255 20755 22648 18272 21447 20842 26797 20556 26791

26058 24393 24475 36263 18957 22648 18957 24475 26797 20432 23803 23018 26797 25760 22364 24661 31524 22648 26058 22078 26791 24001 23656 20680 20432

23464.3 23859 24019 24476 25184 24393 23605 24040 23432 24253 23747 24309 24304 26184 24430 24769 25257 24432 25079 23702 24750 25377 23069 24952 24196

-1.26835 -0.72 -0.49 0.146 1.137 0.03 -1.07 -0.46 -1.31 -0.17 -0.87 -0.09 -0.09 2.534 0.082 0.557 1.238 0.086 0.99 -0.94 0.53 1.406 -1.82 0.811 -0.25

ChartObject Histogram
Last Updated on 3/10/99
By Margaret Jamison

STATE	INCOME (x)	f(x)	f(z)
Alabama ...............	20,842	6.8117E-05	0.2532
Alaska ................	25,305	1.0409E-04	0.3869
Arizona ...............	22,364	9.2552E-05	0.3441
Arkansas ..............	19,585	4.6603E-05	0.1732
California ............	26,570	9.0312E-05	0.3357
Colorado ..............	27,051	8.3005E-05	0.3086
Connecticut ...........	36,263	6.5215E-07	0.0024
Delaware ..............	29,022	4.9320E-05	0.1833
Florida ...............	25,255	1.0443E-04	0.3882
Georgia ...............	24,061	1.0690E-04	0.3974
Hawaii ................	26,034	9.7277E-05	0.3616
Idaho .................	20,478	6.1749E-05	0.2296
Illinois ..............	28,202	6.3374E-05	0.2356
Indiana ...............	23,604	1.0496E-04	0.3902
Iowa ..................	23,102	1.0110E-04	0.3758
Kansas ................	24,379	1.0731E-04	0.3989
Kentucky ..............	20,657	6.4880E-05	0.2412
Louisiana .............	20,680	6.5283E-05	0.2427
Maine .................	22,078	8.8496E-05	0.3290
Maryland ..............	28,969	5.0199E-05	0.1866
Massachusetts ....	31,524	1.6990E-05	0.0632
Michigan ..............	25,560	1.0210E-04	0.3796
Minnesota .............	26,797	8.6968E-05	0.3233
Mississippi ...........	18,272	2.7746E-05	0.1031
Missouri ..............	24,001	1.0674E-04	0.3968
Montana ...............	20,046	5.4279E-05	0.2018
Nebraska ..............	23,803	1.0600E-04	0.3941
Nevada ................	26,791	8.7059E-05	0.3236
New Hampshire ....	28,047	6.6087E-05	0.2457
New Jersey ............	32,654	9.0503E-06	0.0336
New Mexico ........ ..	19,587	4.6635E-05	0.1734
New York ..............	30,752	2.4773E-05	0.0921
North Carolina ........	23,345	1.0318E-04	0.3836
North Dakota ..........	20,271	5.8147E-05	0.2162
Ohio ..................	24,661	1.0702E-04	0.3979
Oklahoma ..............	20,556	6.3112E-05	0.2346
Oregon ................	24,393	1.0731E-04	0.3989
Pennsylvania ..........	26,058	9.6997E-05	0.3606
Rhode Island ..........	25,760	1.0023E-04	0.3726
South Carolina ........	20,755	6.6595E-05	0.2476
South Dakota ..........	21,447	7.8504E-05	0.2918
Tennessee .............	23,018	1.0028E-04	0.3728
Texas .................	23,656	1.0526E-04	0.3913
Utah ..................	20,432	6.0946E-05	0.2266
Vermont ...............	23,401	1.0361E-04	0.3852
Virginia ..............	26,438	9.2157E-05	0.3426
Washington ..........	26,718	8.8155E-05	0.3277
West Virginia .........	18,957	3.6937E-05	0.1373
Wisconsin .............	24,475	1.0728E-04	0.3988
Wyoming ...............	22,648	9.6199E-05	0.3576
m =	24,386	0	0
s =	3755.1	2.8920E-05	0.1075

THEORETICAL STATISTICAL FUNCTION, f(Z)

z-scores	h1=f(z)	h	area	interval	Finding areas:
-3	0.0044	0.5	0.0055	(-2.5 to 3)	Use the area of a trapezoid to
-2.5	0.0175	0.5	0.0179	(-2 to -2.5)	determine area under the curve
-2	0.0540	0.5	0.0459	(-1.5 to -2)	or probabilities for every change
-1.5	0.1295	0.5	0.0929	(-1 to -1.5)	in h or .5 increment in z-scores.
-1	0.2420	0.5	0.1485	(-.5 to -1)
-0.5	0.3521	0.5	0.1878	(0 to -.5)
0	0.3989	0.5	0.1878	(0 to .5)
0.5	0.3521	0.5	0.1485	(.5 to 1)
1	0.2420	0.5	0.0929	(1 to 1.5)
1.5	0.1295	0.5	0.0459	(1.5 to 2)
2	0.0540	0.5	0.0179	(2 to 2.5)
2.5	0.0175	0.5	0.0055	(2.5 to 3)
3	0.0044	0.5

Sample #1	Sample #2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
25255	31524	19585	23345	19585	28969	26438	25305	23656	24379	20478	25255	18957	23018	32654	36263	23604	23345	24475	27051	23102	26797	28047	24001	23102
22648	25760	20432	24475	29022	19587	19585	30752	19585	20842	36263	26570	26034	24061	23604	24061	20842	26791	26797	20842	23345	20478	24475	23018	22364
23345	22364	20478	18957	24661	26797	21447	23656	20680	28969	26797	22364	24001	23401	20657	28047	28047	28047	23018	24393	26718	28047	25255	23604	25760
23018	30752	20755	28969	20271	20432	20657	23803	30752	24393	29022	24475	28969	32654	24475	19587	22648	24001	20657	25560	26797	24393	18957	28202	23018
18272	24061	20657	25560	36263	26791	26034	23604	28047	20046	20842	25760	26791	24001	25305	19585	28202	26034	28202	24061	20046	19585	22078	23102	20556
23401	23803	24001	20432	27051	32654	29022	19587	23018	29022	20755	26797	22648	23803	19587	20046	26438	24379	26718	25305	23604	26034	25305	22078	20842
23656	20271	28969	23656	20556	24661	20432	27051	20046	19585	23656	26718	24661	36263	24393	25560	25760	20478	26791	20556	20432	28202	21447	22648	24661
25760	20657	23803	27051	26034	22078	23803	20046	27051	26034	19585	29022	18272	28202	28047	20755	19585	18957	23102	25255	22364	26438	20432	20657	26797
20680	23656	24393	20478	20842	18272	26058	24061	20271	23604	22648	31524	23345	30752	21447	31524	28969	23401	20046	23018	24001	26570	24001	32654	20680
25560	20556	19587	22078	22364	20680	24475	25560	23604	20478	20556	20046	24475	26570	23401	18957	27051	31524	30752	20271	28969	25760	18272	29022	18957
20755	20842	23102	23018	28969	23401	23345	20657	24379	23656	30752	20432	27051	23656	20271	23401	23401	25760	25305	26718	23803	24475	25560	26718	23803
31524	21447	24061	23102	22648	26718	22364	20755	24661	25760	18272	24001	22078	23102	20842	20657	22078	26570	36263	23604	30752	26718	23803	20842	28202
29022	24475	23018	28202	26797	25255	19587	20432	21447	32654	22364	22078	26058	29022	20432	24379	24001	25560	18957	30752	24061	24661	26034	28047	26570
20842	20755	25255	26034	32654	22364	23102	23102	22648	20657	27051	24661	24379	23345	20755	20432	32654	28969	31524	23656	26058	32654	20680	26791	23656
22078	26438	28047	24661	22078	30752	18272	29022	24475	19587	26438	20680	24393	20432	26438	26570	20680	27051	24379	24001	23656	23345	26570	23656	29022
18957	26058	30752	20755	31524	26058	20680	22078	23345	28202	22078	25560	25305	28969	30752	23102	24661	24061	20271	19587	28047	23401	19585	30752	25255
24475	18272	26034	22364	24379	26034	36263	25760	18272	20755	20657	23345	21447	24661	23102	32654	23018	20271	19587	29022	25760	30752	20842	31524	28969
19587	24379	21447	26718	18272	23656	20046	26718	25255	25255	19587	23401	22364	25560	36263	30752	26718	20046	26034	20046	25255	24379	19587	20478	24475
24393	26718	31524	23401	30752	20046	31524	24379	20657	30752	23345	20478	28047	26438	23803	24393	25255	20755	22648	18272	21447	20842	26797	20556	26791
26058	24393	24475	36263	18957	22648	18957	24475	26797	20432	23803	23018	26797	25760	22364	24661	31524	22648	26058	22078	26791	24001	23656	20680	20432
23464.3	23859	24019	24476	25184	24393	23605	24040	23432	24253	23747	24309	24304	26184	24430	24769	25257	24432	25079	23702	24750	25377	23069	24952	24196
-1.26835	-0.72	-0.49	0.146	1.137	0.03	-1.07	-0.46	-1.31	-0.17	-0.87	-0.09	-0.09	2.534	0.082	0.557	1.238	0.086	0.99	-0.94	0.53	1.406	-1.82	0.811	-0.25