Z Values

Z value formula
1. compute y = 1 / (1 + .2316419 * abs(Z) )
2. x = 1 - .3989423 * e^(-Z^2) *
(1.330274 * y^5 -
1.821256 * y^4 +
1.781478 * y^3 -
.356538 * y^2 +
.3193815 * y)

3. if Z > 0, prob = x, else 1 - x

Z Value spreadsheet formula
1. label Z
2. copy into cell y:
+1/(1+.2316419*@abs(Z))
3. label this y
4. copy into cell x:
+1-.3989423*@exp(-Z^2/2)*(1.330274*y^5-1.821256*y^4+
1.781478*y^3-.356538*y^2+.3193815*y)

3. if Z > 0, prob = x, else 1 - x

Z Value summary:
prob of stock moving up:
.67 SD = 25.1%
1 SD = 15.9%
1.5 SD: 7.7%
2 SD = 2.3%

%ile: = mean +:
95th 1.65 SD
90th 1.28 SD
75th 0.675 SD
25th -0.675 SD
10th -1.28 SD
5th -1.65 SD

prob of bw +/-:
1 SD = 68.3%
1.65 SD = 90.0%
2 SD = 95.5%

prob of below
1 SD = 84.1%
1.29 = 90.3%
1.5 = 93.3%
2 SD = 97.7%


Z values
Z: cum prob: Expd if less than or equal to:
3 .0013 3
2.5 .0062 2.58
2.0 .0228 2.15
1.5 .0668 1.70

1.0 .1587 1.30
0.5 .3085 0.91

0 .5000 0.56
-.5 .6915 0.30
-1.0 .8414 0.14

-1.5 .9332 0.05
-2.0 .9772 0.02
-3.0 .9986