An insurance company receives 100 claims per day on average. Claims arrive independently and at random at the company office. Of the claims, 95% are for amounts less than $100 and are processed immediately; the remaining 5% are examined more closely to verify their accuracy and eligibility.
a. What is the probability of getting no claims over $100 in a given day?
b. What is the probability of getting at most two claims over $100 in a given day?
c. How many claims for amounts les than $100 should this company expect to receive in 5 business days?