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A school is watching students as they enter the football game for students who are dressed
inappropriately. they estimate that 7% of all students are dressed inappropriately. out of a group
of 40 students, what is the probability that exactly 2 are dressed inappropriately? round to 3 decimal places.

Respuesta :

Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

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 values of the parameters are given as follows:

n = 40, p = 0.07.

The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:

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

[tex]P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242[/tex]

0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

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

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