The problem:W N100, 225,P112 W 126

1
The problem W N(100, 225), P(112 lt W lt 126)
?
Preliminary (how many iterations?) 1. 95
Confidence (standard value) 2. Area 0.28
(find the right box) 3. Margin of error
0.005 (desired accuracy) 4.
2
Pseudo-code (Algorithm)
1. S 0, n 0 (initialize) 2. X Unif(112,
126) 3. Y Unif(0, 0.02) 4. Function 5. If
Y lt Function then Check 1, otherwise Check
0 6. If Check 1 then S S 1 7. n n 1 8.
Have we done enough iterations? If no then go to
step 2 9. Stop
3
Output
(estimated proportion of box that is filled)
(estimated area under the function)
(estimated margin of error)
(1 a)100 CI for area
4
The problem What is the volume of a sphere
centered at (5, -3, 8) with radius 4?
Preliminary (how many iterations?) 1. 95
Confidence (standard value) 2. Volume 83 512
(find the right box) 3. Margin of error
5 (desired accuracy) 4.
5
Pseudo-code (Algorithm)
1. S 0, n 0 (initialize) 2. X Unif(1, 9) 3.
Y Unif(-7, 1) 4. Z Unif(4, 12) 5. Function
(x 5)2 (y 3)2 (z 8)2 - 16 6. If Function
lt 0 then Check 1, otherwise Check 0 7. If
Check 1 then S S 1 8. n n 1 9. Have we
done enough iterations? If no then go to step
2 10. Stop
6
Output
(estimated proportion of box that is filled)
(estimated area under the function)
(estimated margin of error)
(1 a)100 CI for volume