X |
Z=(X-100)/8 |
N(Z) |
70 |
-3.75 |
1-0.9999=0.0001 |
84 |
-2 |
1-0.9772=0.0228 |
92 |
-1 |
1-0.8413=0.1587 |
98 |
-0.25 |
1-0.5987=0.4013 |
108 |
1 |
0.8413 |
112 |
1.5 |
0.9332 |
116 |
2 |
0.9772 |
124 |
3 |
0.9987 |
The diagrams (not to scale) below symbolically explain the arithmetic.
P(X>108)=1-0.8413=0.1587
P(X<98)=0.4013
P(92<X<108)=0.8413-0.1587=0.6826
P(84<X<116)=0.9772-0.0228=0.9544
P(X<84)=0.0228