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The probability of being a universal donor is 6% (O-negative-blood type). Suppose that 6 people come to a blood drive.
a) What are the mean and standard deviation of the number of universal donors among the 6 people?
b) What is the probability that there are exactly three universal donors?

Respuesta :

Using the binomial distribution, it is found that:

a) The mean is of 0.36 and the standard deviation is of 0.58.

b) There is a 0.0036 = 0.36% probability that there are exactly three universal donors.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The values of the parameters are given as follows:

n = 6, p = 0.06.

Item a:

  • E(X) = np = 6 x 0.06 = 0.36.
  • [tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6 \times 0.06 \times 0.94} = 0.58[/tex]

The mean is of 0.36 and the standard deviation is of 0.58.

Item b:

The probability is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{6,3}.(0.06)^{3}.(0.94)^{3} = 0.0036[/tex]

There is a 0.0036 = 0.36% probability that there are exactly three universal donors.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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