The time in months between occurrences of safety violations in a toll manufacturing facility is shown in the table below.
|
1.31
|
0.15
|
3.02
|
3.17
|
4.84
|
0.71
|
0.70
|
1.41
|
2.68
|
0.68
|
|
1.94
|
3.21
|
2.91
|
1.66
|
1.51
|
0.30
|
0.05
|
1.62
|
6.75
|
1.29
|
|
0.79
|
1.22
|
0.65
|
3.90
|
0.18
|
0.57
|
7.26
|
0.43
|
0.96
|
3.76
|
(i) Determine the mean, median and variance for this sample data. Construct a histogram and explain why the observed shape is not surprising, given the nature of the phenomenon in question.
(ii) What is a reasonable probability model for the population from which the data came? If the population parameter, the mean time between violations, is postulated to be 2 months, compute the theoretical probability of going more than 2 months without a safety violation. Is this theoretical probability compatible with this sample data? Explain.
(iii) In actual fact, the data were obtained for three di?erent operators and have been arranged accordingly: the ?rst row is for "Operator A," the second row, for "Oper- ator B," and the third row for "Operator C." It has been a long-held preconception in the manufacturing facility that "Operator A" is relatively more safety-conscious than the other two. Strictly on the basis of any graphical and numerical descriptions of each data set that you deem appropriate, is there any "suggestion" in this data set that could potentially support this preconception? Explain.