5.3 Exercise 57

Use the following information to answer the next three exercises. The average lifetime of a certain new smartphone is three years. The manufacturer will replace any smartphone failing within two years of the date of purchase. The lifetime of these smartphones is known to follow an exponential distribution.

According to the American Red Cross, about one out of nine people in the U.S. have Type B positive blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B positive blood types that arrive roughly follows the Poisson distribution.

1. If 100 people arrive, how many on average would be expected to have Type B positive blood?
2. What is the probability that over 10 people out of these 100 have type B positive blood?
3. What is the probability that more than 20 people arrive before a person with type B positive blood is found?