Assignment Problem:
(a) The following table shows data collected on the time to failure (in days) for a particular machine at a manufacturing plant. Plot the histogram using an interval width of 3 days.
| 79.919 |
3.027 |
6.769 |
18.387 |
144.7 |
0.941 |
0.624 |
0.59 |
7.004 |
3.217 |
| 3.081 |
6.505 |
59.899 |
0.141 |
2.663 |
0.878 |
5.38 |
1.928 |
31.764 |
14.382 |
| 0.006 |
0.021 |
1.192 |
43.567 |
17.967 |
3.371 |
3.315 |
0.3 |
1.005 |
1.008 |
| 1.961 |
0.013 |
34.76 |
24.42 |
0.091 |
2.157 |
7.078 |
0.002 |
1.14 7 |
2.236 |
| 5.845 |
0.123 |
5.009 |
0.443 |
9.003 |
7.579 |
23.96 |
0.543 |
0.219 |
4.567 |
Identify the appropriate distribution based on the shape of the histogram you have obtained. Calculate the estimator for this distribution.
(b) Suppose you have a limited dataset of ratio of customer complaints on 5 days as follows: 0.27, 0.54, 0.87, 0.12 and 0.92. Make an assumption about the distribution of customer complaints.
Analyse the goodness-of-?t of your selected distribution using the Q-Q plot. Discuss your ?ndings.