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

Probability that x is less than or equal to 1 = 0.5551

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)`

=
`(20!)/((20!)(0!)).072^(0)0.928^(20 - 0)` +
`(20!)/((19!)(1!)).072^(1)0.928^(20 - 1)`

= 0.22436 + .33074

= 0.5551