Homework #2
5.3
The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation of the flaws.
|
Flaws |
Probability |
|
0 |
0.461 |
|
1 |
0.283 |
|
2 |
0.129 |
|
3 |
0.087 |
|
4 |
0.038 |
The mean or expected value is:
µ
= E(x) = 
The standard deviation is:
= 
|
x |
P(x) |
|
0 |
0.461 |
|
1 |
0.283 |
|
2 |
0.129 |
|
3 |
0.087 |
|
4 |
0.038 |
|
x |
P(x) |
µ or E(x) |
(x - µ)2 |
(x - µ)2 . P(x) |
|
0 |
0.461 |
0.00000 |
0.00000 |
0.00000 |
|
1 |
0.285 |
0.28500 |
0.51123 |
0.14570 |
|
2 |
0.129 |
0.25800 |
3.03456 |
0.39146 |
|
3 |
0.087 |
0.26100 |
7.50212 |
0.65268 |
|
4 |
0.038 |
0.15200 |
14.80710 |
0.56267 |
|
|
µ = |
0.95600 |
|
1.75251 |
|
|
SD = |
1.32382 |
|
|
