contestada

10. A company finds that 45% of first-time visitors to its website do not buy any of its products. If there are 75 first-time visitors on a given day, what is the probability that exactly 36 of them buy a product? Round your answer to the nearest thousandth. Answer choices: 0.044 0.080 0.450 0.550

Respuesta :

Using the binomial distribution, it is found that the probability that exactly 36 of them buy a product is of 0.044.

For each first-time visitor, there are only two possible outcomes, either they buy a product, or they do not. The probability of a first-time visitor buying a product is independent of any other first-time visitor, hence the binomial distribution is used to solve this question.

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:

  • 45% of first-time visitors to its website do not buy any of its products, hence 55% buy, that is, p = 0.55.
  • There are 75 first-time visitors on a given day, hence n = 75.

The probability that exactly 36 of them buy a product is P(X = 36), hence:

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

[tex]P(X = 36) = C_{75,36}.(0.55)^{36}.(0.45)^{39} = 0.044[/tex]

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