People with O-negative blood are called “universal donors” because O-negative blood can be given to patients with any blood type. However, only about 6% of people have O-negative blood, which presents a challenge in balancing supply and demand made more complicated not only by the logistics of finding donors that meet health criteria, but also by the fact that the blood type of donor and patient must be matched. This is especially true, since, unlike a manufacturer who can balance supply by planning to produce or to purchase more or less of a key item, blood supply from volunteer donors show up more-or-less at random (at least in terms of blood type). Thus, modeling the arrival of samples with various blood types helps humanitarian organizations, such as the Philippine Red Cross, to plan their blood allocations. Of the next 20 donors to arrive at Philippine Red Cross, how many universal donors can be expected? (Answer in 1 decimal place) What is the standard deviation of the number of universal donors? (Answer in 2 decimal places)  What is the probability that there are exactly 2 or 3 universal donors out of the 20 donors to arrive at Philippine Red Cross? (Answer in 4 decimal places)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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People with O-negative blood are called “universal donors” because O-negative blood can be given to patients with any blood type. However, only about 6% of people have O-negative blood, which presents a challenge in balancing supply and demand made more complicated not only by the logistics of finding donors that meet health criteria, but also by the fact that the blood type of donor and patient must be matched. This is especially true, since, unlike a manufacturer who can balance supply by planning to produce or to purchase more or less of a key item, blood supply from volunteer donors show up more-or-less at random (at least in terms of blood type). Thus, modeling the arrival of samples with various blood types helps humanitarian organizations, such as the Philippine Red Cross, to plan their blood allocations.

Of the next 20 donors to arrive at Philippine Red Cross, how many universal donors can be expected? (Answer in 1 decimal place)

What is the standard deviation of the number of universal donors? (Answer in 2 decimal places) 

What is the probability that there are exactly 2 or 3 universal donors out of the 20 donors to arrive at Philippine Red Cross? (Answer in 4 decimal places)

Interpret your results in two sentences only.

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