Question 7 (10 marks) A company has 1,000 employees who are partly covered under a disability insurance plan. The plan pays full salary for up to 4 weeks of disability (after which a government plan takes over). Occurrence of disability among employees are independent of one another, and an employee is covered for only one occurrence per year. The following information is known: Employee Category 1 2 Weekly Salary 400 600 800 Number of Employees 300 500 200 Disability Probability 0.025 0.02 0.01 3 Length of Disability 1 week 2 weeks 3 weeks 2 4 weeks Probability 0.8 0.1 0.05 0.05 The company actuary calculate the annual premium required to ensure (using the normal approximation) with 95% probability that the premium will exceed disability claims. What percentage of total weekly payroll is that premium? Question 7 (10 marks) A company has 1,000 employees who are partly covered under a disability insurance plan. The plan pays full salary for up to 4 weeks of disability (after which a government plan takes over). Occurrence of disability among employees are independent of one another, and an employee is covered for only one occurrence per year. The following information is known: Employee Category 1 2 Weekly Salary 400 600 800 Number of Employees 300 500 200 Disability Probability 0.025 0.02 0.01 3 Length of Disability 1 week 2 weeks 3 weeks 2 4 weeks Probability 0.8 0.1 0.05 0.05 The company actuary calculate the annual premium required to ensure (using the normal approximation) with 95% probability that the premium will exceed disability claims. What percentage of total weekly payroll is that premium