Final answer:
Duchess Cruise Lines can expect to gross $4.99925 on one trip insurance policy for their Mediterranean cruise, after considering the refund rate of 0.15 per thousand passengers.
Step-by-step explanation:
The student's question concerns how much Duchess Cruise Lines can expect to gross on one policy for trip insurance on their Mediterranean cruise.
The data provided states that there are 0.15 refunds per thousand passengers. Given that the insurance cost per passenger is $5, we can calculate the expected gross income per policy by considering the probability of a refund. The refund rate of 0.15 per thousand means that for every 1,000 passengers, 0.15 refunds are expected. Since the premium cost per passenger is $5, the gross amount includes this premium minus the expected cost of the refund.
To get the expected gross amount, we multiple the premium by the probability that the insurance will not be used, which is 1 - (0.15/1000). This gives us an expected gross per policy: $5 × (1 - 0.00015) = $4.99925.