Answer:
Probability that x is less than or equal to 1 = 0.5551
Step-by-step explanation:
Given -
People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood.
Probability of sucess (population has O-negative blood ) = p = 7.2% = .072
Probability of failure ( q) = 1 - p = 1 - .072 = 0.928
Sampe size ( n ) = 20
Let X denote the number of universal donors among them
probability that x is less than or equal to 1 =
[tex]P( X \leq 1)[/tex] = [tex]P( X = 0) + P( X = 1)[/tex] ( Using binomial distribution)
= [tex]\binom{20}{0}.072^{0}0.928^{20 - 0} + \binom{20}{1}.072^{1}0.928^{20 - 1}[/tex]
= [tex]\frac{20!}{(20!)(0!)}.072^{0}0.928^{20 - 0}[/tex] + [tex]\frac{20!}{(19!)(1!)}.072^{1}0.928^{20 - 1}[/tex]
= 0.22436 + .33074
= 0.5551
