##### Scenario Weather-insurance portfolio profitability. ##### Question Given: premium $30/month paid 12 months upfront, servicing cost $3/month, benefit cost $8 000/claim, regulatory cost $4/quarter plus $300 per claim. What claim rate yields breakeven? Four customer segments A–D have different cumulative claim risks. Which combination maximizes profit and why? After choosing segments, illustrate how adding B, C, and D changes profit compared with only A. ##### Hints Compute expected value per policy; select segments with positive expected profit.

This question evaluates expected-value and breakeven calculations, cost modeling, and segment-level profitability analysis within the Statistics & Math domain for a data scientist role.

How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Onsite rounds at Capital One.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Determine Claim Rate for Breakeven in Insurance Portfolio

Weather-Insurance Portfolio Profitability

Setup

You price a 12-month weather insurance policy. Customers pay premiums upfront for the year. Each policy can generate regulatory and servicing costs, and possibly a claim. Assume at most a small expected number of claims per policy-year (treat the "claim rate" as the expected number of claims per policy-year; if at most one claim occurs, this equals the annual claim probability).

Premium: $30 per month, paid for 12 months upfront.
Servicing cost: $3 per month.
Benefit (indemnity) per claim: $8,000.
Regulatory cost: $4 per quarter, plus$ 300 per claim.

Tasks

What claim rate yields breakeven on a per-policy annual basis?
You have four customer segments A–D with different annual claim rates (expected claims per policy-year): r_A, r_B, r_C, r_D. Which segment combination maximizes profit, and why? State the rule you would use.
After choosing the optimal set of segments, illustrate how adding B, C, and D changes profit compared with offering only to A. Show both a general formula (per policy and with policy counts if available) and a small numeric example to make it concrete.

Assumptions

Costs given are per policy unless noted.
Ignore time value of money since premiums are paid upfront and no discount rate is specified.
Regulatory cost " $4/quarter" is per policy (so$ 16 per policy-year).

Setup

Premium: $30 per month, paid for 12 months upfront.

Servicing cost: $3 per month.

Benefit (indemnity) per claim: $8,000.

Regulatory cost:

4 per quarter, plus

300 per claim.

Tasks

What claim rate yields breakeven on a per-policy annual basis?

You have four customer segments A–D with different annual claim rates (expected claims per policy-year): r_A, r_B, r_C, r_D. Which segment combination maximizes profit, and why? State the rule you would use.

After choosing the optimal set of segments, illustrate how adding B, C, and D changes profit compared with offering only to A. Show both a general formula (per policy and with policy counts if available) and a small numeric example to make it concrete.

Determine Claim Rate for Breakeven in Insurance Portfolio

Quick Overview

Weather-Insurance Portfolio Profitability

Setup

Tasks

Assumptions

Solution

Submit Your Answer to Earn 20XP

Determine Claim Rate for Breakeven in Insurance Portfolio

Quick Overview

Weather-Insurance Portfolio Profitability

Setup

Tasks

Assumptions

Solution

Submit Your Answer to Earn 20XP