4) A group health insurance provider has just sold a group health plan to a new employer.On the basis of limited underwriting, there is a 30% chance the group will

turn out to be a high utilizer. High-utilization groups average 50 claims per month, and low-utilization groups average 20 claims per month. The number of claims on a group for which the utilization is known follows a Poisson distribution. Determine the probability that the group submits1

Fig: 1