An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 The Manager provides the following utility function to evaluate the two stores. xi 0 1 2 3 4 5 6 u(xi) 1.00 0.60 0.40 0.20 0.10 0.05 0.00 Which store does the Manager prefer as having fewer complaints? Compare using utility as the metric with using the average number of complaints as the criterion for deciding which Store is better (or worse). Why?
An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints.
Store A
|
xi |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
p(xi) |
0.10 |
0.15 |
0.20 |
0.25 |
0.15 |
0.10 |
0.05 |
|
Store B |
|
|
|
|
|
|
|
|
xi |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
p(xi) |
0.10 |
0.15 |
0.25 |
0.22 |
0.13 |
0.08 |
0.07 |
The Manager provides the following utility
|
xi |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
u(xi) |
1.00 |
0.60 |
0.40 |
0.20 |
0.10 |
0.05 |
0.00 |
Which store does the Manager prefer as having fewer complaints? Compare using utility as the metric with using the average number of complaints as the criterion for deciding which Store is better (or worse). Why?
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