So I'm stuck on finding the most efficient way to approach this homework problem.
In a certain population, 15% of the people have Rh-negative blood. A blood bank serving this population receives 100 blood donors on a particular day.
a. Let X be the number of donors in the sample with Rh-negative blood. What is the
exact distribution of X?
So I'm assuming in order to solve this question, I'm supposed to do something like:
P(x=0) = ( 100 C 0 )*(15/100)^0 (85/100)^100
P(x = 1) = (100 C 1) (15/100)^1(85/100)^99
P(x = 2) = (100 C 2)*(15/100)^2 (85/100)^(98)
….
But that seems like an awful lot of steps for one question. Is there a quicker way to answer this question wihout using combinations? Should I not be using binomial distribution?
Update: After doing some searching I found a thread with a similar question. Someone commented using poisson distribution and I was wondering if that would work? Exact and approximate probability distribution
Best Answer
Comment in Answer format to permit a graph.
Assuming that participation does not change with blood type, the number with Rh negative blood will be $X \sim \mathsf{Binom}(n = 100, p=0.15).$
In R statistical software a binomial PDF is called
dbinom
, so the formula in @ sasquire' comment is as shown in the code below, used to make the figure.Because $P(X > 30) \approx 0,$ that part of the graph is not shown.