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A Gallup survey showed that in March 2011 , 8v of every 25 employers in the United States were adding more workers to their workforce, 9 of 50 were reducing their workforce, and 1 of 2 were keeping it the same. In a metropolitan area there are 1250 employers and of those who will hire, they will hire an average of seven new employees. If the employers who were cutting their workforce in that area were planning on letting go an average of nine workers, what would the net change in jobs for the area be?

Answer :

Using the expected value, it is found that the net change in jobs for the area would be of 775.

  • The expected value is given by the sum of each outcome multiplied by it's probability.

In this problem:

  • [tex]\frac{8}{25} = \frac{16}{50}[/tex] probability of an addition of 7 employees to the workforce.
  • [tex]\frac{9}{50}[/tex] probability of a reduction of 9 employees to the workforce.

The net change, as a proportion, is:

[tex]E(X) = 7\frac{16}{50} - 9\frac{9}{50} = \frac{7(16) - 9(9)}{50} = 0.62[/tex]

Out of 1250 employers:

[tex]0.62(1250) = 775[/tex]

The net change in jobs for the area would be of 775.

A similar problem is given at https://brainly.com/question/24855677

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