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In a survey of 320 college graduates, 36% reported that they stayed on their first full-time job less than 1 year. If 15 of those subjects are randomly selected without replacement for a follow-up survey, find the probability that exactly 5 of them stayed on their job for less than one-year.
Name the variables in the context of the problem.
State the requirements for binomial distribution for this problem.
Use the long formula above to find P(x)

Respuesta :

Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.

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, there is a fixed number of independent trials, each with only two possible outcomes, hence the binomial distribution is used. The values of the parameters are:

n = 15, p = 0.36.

The probability is P(X = 5), hence:

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

[tex]P(X = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094[/tex]

0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.

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

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