Question

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. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them. assume that x follows a binomial distribution. the probability that x is less than or equal to 1 is

Answer 1

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 =

$P( X \leq 1)$ = $P( X = 0) + P( X = 1)$                 ( Using  binomial distribution)

               = $\binom{20}{0}.072^{0}0.928^{20 - 0} + \binom{20}{1}.072^{1}0.928^{20 - 1}$              

               = $\frac{20!}{(20!)(0!)}.072^{0}0.928^{20 - 0}$ + $\frac{20!}{(19!)(1!)}.072^{1}0.928^{20 - 1}$

               = 0.22436 + .33074

               = 0.5551