Answer:
about $145.33
Step-by-step explanation:
Consider a group of 15 customers. They will pay ...
15 × $258 = $3870
in premiums each year.
One-third of those, 5 customers, will submit claims for fillings, so will cost the insurance company ...
5 × $110 = $550
And 80% of them, 12 customers, will submit claims for preventive check-ups, so will cost the company ...
12 × $95 = $1140
The net income from these 15 customers will be ...
$3870 -550 -1140 = $2180
Then the average income per customer is this value divided by the 15 customers in the group:
$2180/15 = $145.33
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<em>Alternate solution</em>
Above, we chose a number of customers that made 1/3 of them and 4/5 of them be whole numbers. You can also work with one premium and the probability of a claim:
258 - (1/3)·110 - 0.80·95 = 145.33
