An automobile owner has 40% chance of having exactly one accident in a year and 60% chance of having no accidents in a year. There is no chance that the automobile owner incurs more than one accident in a year. If there is an accident, the loss amount has the following distribution:
Loss Amount Probability
30 0.30
60 0.15
100 0.45
180 0.10
Suppose there is an ordinary deductible of $40 and the maximum payment by the insurer is $130.
Determine the standard deviation of the payment made by the insurer to the automobile owner.
A: 32.44
B: 33.60
C: 34.77
D: 26.78
E: 27.43