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Question 2 of 21
In Accra, 30% of workers owns a car. In a sample of 10 workers, what is the probability that exactly three workers owns a car?
O A. 0.267
OB. 0.65
O C. 0.48
O D.0.73

Respuesta :

Using the binomial distribution, it is found that the probability that exactly three workers owns a car is given by:

A. 0.267.

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.

In this problem:

  • 30% of workers owns a car, hence p = 0.3.
  • A sample of 10 workers is taken, hence n = 10.

The probability that exactly three workers owns a car is given by P(X = 3), hence:

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

[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.267[/tex]

Hence option A is correct.

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

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