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Sixty-one percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

Respuesta :

The unusual outcomes for the binomial distribution are given as follows:

0 or 1 employee making judgements.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each 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]

In the binomial distribution, a measure is considered unusual if it is more than 2.5 standard deviations from the mean.

For this problem, the parameters are given as follows:

n = 8, p = 0.61.

Hence the mean and the standard deviation are given by:

  • E(X) = np = 8 x 0.61 = 4.88.
  • [tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8(0.61)(0.39)} = 1.38[/tex]

The bounds of usual outcomes are:

  • 4.88 - 2.5 x 1.38 = 1.43.
  • 4.88 + 2.5 x 1.38 = 8.33.

Hence outcomes of less than 1 employee making judgements would be unusual.

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

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