Question

3. People with type O-negative blood are universal donors (any patient can

receive a transfusion of O-negative blood). Only about 6.6% of the American
population has O-negative blood. If 270 unrelated people give blood in a certain
week, how many of these people do we expect to be universal donors? (Hint:
Remember to convert percent numbers to decimals before multiplying.)
PLEASE HELP

Answer 1

We expect 17.82, that is, approximately 18 people to be universal donors.

Explanation:

For each person, there are only two possible outcomes. Either they are universal donors, or they are not. The probability of a person being an universal donor is independent of any other person. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

`E(X) = np`

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

Only about 6.6% of the American population has O-negative blood.

This means that
`p = 0.066`

If 270 unrelated people give blood in a certain week, how many of these people do we expect to be universal donors?

This is E(X) when
`n = 270`. So

`E(X) = np = 270*0.066 = 17.82`

We expect 17.82, that is, approximately 18 people to be universal donors.