Question

Suppose the insurance company knows that there might be some amount of error from their prediction in the previous question. If the estimate follows a normal distribution and has a standard deviation of $500, what are the chances that the insurance company will lose money (assuming administrative expenses are 0) this year?

PLEASE ANSWER THE QUESTION ABOVE. THE ONE BELOW IS ONLY BACKGROUND INFORMATION

Suppose that an insurance company covers an organization with members from two population groups: healthy and sick. The healthy population group averages $2,000 in healthcare expenditures annually while the sick population group averages $50,000 in expenditures. If the insurance company believes 90% of the organization consists of healthy individuals, what is the average expected spending for the members? If the health insurance company adds a 10% loading factor onto the average costs to cover administrative expenses, what is the average charge per person for the organization

Answer 1

Expected average spending per member = 0.9 * 2000 + 0.1 * 50000 = 6800$

Assuming 0 administrative expenses as the question specifies, and that the estimate follows a normal distribution,

Mean of the normal distribution = 6800

Hence, the estimate , say X has the distribution, X ~ N(6800, 500²)

X <= 0 corresponds to Z-score of (X - mean)/StdDev = (0 - 6800)/500 = -13.6

Looking up the Z-score table, P(Z <= -13.6) 0

Hence, probability of insurance company losing money = P(X<=0) = 0