Question

Suppose that there are 100 young people looking to buy health insurance. They consist of the following: 20 people that like to ride motorcycles, each willing to pay $2,500 20 people that like to ski, each willing to pay $2,200 20 people that like to skateboard each willing 10 pay $1,800 20 people that hike to ride bicycles, each willing to pay $1,200 10 people that like to hike, each willing to pay $1,000 10 people that like to take yoga classes, each willing to pay $800 Assume that the insurance company does not know the activities that individuals enjoy doing in their leisure time. They do know that, on avenge: Those that like to ride motorcycles will cost, on average, $2,200 Those that like to ski will cost, on average, $2,000 Those that like to skateboard will cost, on average, $1.500 Those that like to ride bicycles will cost, on average, $1,000 Those that like to hike will cost, on average, $600 Those that like to take yoga classes will cost, on average, $700 a) What is the actuarially fair premium for this pool of 100 people?

Answer 1

The actuarially fair premium for this pool of 100 people is $1,452.

Step-by-step explanation:

To determine the actuarially fair premium for this pool of 100 people, we need to calculate the average cost of insurance for each activity group and then multiply it by the number of people in each group. The average cost of insurance for each group is as follows:

• Motorcycle riders: $2,200
• Skiers: $2,000
• Skateboarders: $1,500
• Bicyclists: $1,000
• Hikers: $600
• Yoga practitioners: $700

We can calculate the actuarially fair premium by multiplying the average cost of insurance for each group by the number of people in that group, summing up the results, and then dividing by the total number of people in the pool (100). The actuarially fair premium for this pool of 100 people is $1,452.