Elementary statistics

Question

Assume 43% of us have group O blood. A hospital is conducting a blood drive because it’s supply of group O blood is low, and it needs at least 196 donors of group O blood. If 446 volunteers donate blood, estimate the probability that the number with group O blood is at least 196. Is the pool of 446 volunteers likely to be sufficient?

Answer 1

This is an example of a Binomial Distribution. The probability of success (having a group O blood) is 0.43 and the probability to get at least 196 people with group O blood from the pool of 446 volunteers is given by:

P(X≥196) = sum from x =196 to x=446 of (446 choose x)(0.43)^x(1-0.43)^(446-x) = 0.36

Therefore, the volunteers are not likely to be sufficient.