Question

The most common human blood group is OO which is estimated to be 45% in US population. If you randomly sample 5 people from the US population and test their blood group,

(a) what is the probability that exactly 3 of them have type OO blood?

(b) what is the mean and standard deviation of the number of people with blood type OO?

Answer 1

(a) what is the probability that exactly 3 of them have type OO blood?

Solution:

We are given

n = 5

p = 0.45

q = 1 – p = 1 – 0.45 = 0.55

We have to find P(X=3)

P(X=x) = nCx*p^x*q^(n – x)

P(X=3) = 5C3*0.45^3*0.55^(5 – 3)

P(X=3) = 10*0.45^3*0.55^2

P(X=3) = 0.275653

Required probability = 0.275653

Part b

Mean = np = 5*0.45 = 2.25

Standard deviation = sqrt(npq) = sqrt(5*0.45*0.55) = 1.11243