Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B? Be sure to state and justify your assumptions.

Question

mathmale · Answer

Have you tried identifying the type of probability distribution involved in this problem?

Hints:  n = 80; probability of "success," p = .15.

"Between 15% and 20% of the donors" signifies (.15)(80) = 12 and (.20)(80) = 16.  Thus, we are asked what the total (cumulative) probability is that 12, 13, 14, 15 or 16 donors will have blood type B.

Again:  which probability distribution are we speaking of?

anonymous · Answer

not sure, all i know is something about normal distribution @mathmale

anonymous · Answer

so do i add up all the probabilities? not sure what to do

anonymous · Answer

@mathmale

mathmale · Answer

Sorry for the delay in responding back.  

Unless I'm sorely mistaken, the probability distribution in question is the BINOMIAL.  The binomial distribution applies when n (the number of trials) is an integer, when the probability of success (which in this case would be the probability of a given donor having Type B blood) is given/known, and every trial is independent of every other trial.
Please look up the BINOMIAL DISTRIBUTION for further info, or ask more questions.

Now to answer your question, "do I add up all the probabilities?"  Yes, that's exactly right.  Calculate the binomial probability of 12 donors having Type B blood (out of 80), that of 13, and so on, up to 16 donors out of 80.  Add these five probabilities together; the result is the solution to this problem.

If you have a TI-84 calculator (or similar), you could use the built-in function binompdf for each of these 5 calculations.  Better yet, you could reduce the work involved by using the binomcdf function.  Again, if you have further questions, please ask.