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Nearly 7,000 children acquired disease Z in the last year. Among the population of all children who acquired disease Z in the last year, suppose that (unknown to researchers) 1400 of them (20%) also acquired a secondary skin infection. A researcher intends to take a simple random sample of 50 children who had the disease last year and record whether or not the person also had a secondary infection. Let X be the number of children in the sample who report having a secondary infection. The variance of this distribution is __________

Sagot :

Using the binomial distribution, it is found that the variance is of 8.

For each children, there are only two possible outcomes, either they develop the secondary skin infection, or they do not. The probability of a children developing the secondary skin infection is independent of any other children, hence the binomial distribution is used to solve this question.

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 variance is given by:

[tex]V(X) = np(1-p)[/tex]

In this problem:

  • 50 kids were sampled, hence n = 50.
  • 20% of kids acquire the infection, hence p = 0.2.

Then:

[tex]V(X) = 50(0.2)(0.8) = 8[/tex]

The variance is of 8.

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

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