Question

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

a. True

b. False

Answer 1

The number of people with type B blood arriving at a blood drive does not follow the Poisson distribution. A binomial distribution or geometric distribution is more appropriate as they represent binary outcomes in independent trials and the number of trials until a success, respectively.

Step-by-step explanation:

The assertion that the number of type B blood types that arrive at a blood drive roughly follows a Poisson distribution is incorrect. This situation better fits the criteria for a geometric or binomial distribution, as Poisson distribution usually models the number of occurrences of an event in a fixed interval of time or space, and the occurrences must be independent of each other.

The number of people with Type B blood arriving at a blood drive would be modeled more accurately by a binomial distribution because the outcomes (whether or not a person has Type B blood) are binary and the probability of each person having Type B blood is independent of others and remains constant at 1 out of 9.

In the case where we are looking at the number of people who arrive before a person with Type B blood, we would use a geometric distribution because it describes the number of trials until the first success in a series of independent Bernoulli trials.