Divide the population of U.S. workers into two categories: those who have a job in the goods-producing industries, and those who have a job in the service-producing industries. Among all workers, sixteen percent have a job in the goods-producing industries. For these workers, the mean of annual earnings equals $ 42 , 419, with a standard deviation of $ 35 , 572. Among all workers, the remaining eighty-four percent have a job in the service-producing industries. For these workers, the mean of annual earnings equals $ 36 , 976, with a standard deviation of $ 31 , 247. Find the mean and standard deviation of annual earnings among all workers in the population.Is this the correct answer:Pop mean ( .16 ∗ 42 , 419 ) + ( .84 ∗ 36 , 976 ) = 37 , 846.88Pop StdDev ( .16 ∗ 35 , 572 ) + ( .84 ∗ 31 , 247 ) = 31 , 939

Question

Divide the population of U.S. workers into two categories: those who have a job in the goods-producing industries, and those who have a job in the service-producing industries. Among all workers, sixteen percent have a job in the goods-producing industries. For these workers, the mean of annual earnings equals   $  42  ,  419, with a standard deviation of   $  35  ,  572. Among all workers, the remaining eighty-four percent have a job in the service-producing industries. For these workers, the mean of annual earnings equals   $  36  ,  976, with a standard deviation of   $  31  ,  247. Find the mean and standard deviation of annual earnings among all workers in the population.Is this the correct answer:Pop mean   (  .16  ∗  42  ,  419  )  +  (  .84  ∗  36  ,  976  )  =  37  ,  846.88Pop StdDev   (  .16  ∗  35  ,  572  )  +  (  .84  ∗  31  ,  247  )  =  31  ,  939

timmeraared · Accepted Answer

Let   X be the income of a randomly chosen worker in the goods-producing sector, and let   Y be the income of a randomly chosen worker in the service-producing sector. Then the income   W of a randomly chosen worker is given by  W  =  (  0.16  )  X  +  (  0.84  )  Y  .It follows that  E  (  W  )  =  (  0.16  )  E  (  X  )  +  (  0.84  )  E  (  Y  )  .If we (reasonably) assume independence then  Var  (  W  )  =  (  0.16      )    2    Var  (  X  )  +  (  0.84      )    2    Var  (  Y  )  .For the standard deviation calculation, use the fact that the standard deviation is the square root of the variance.

cazinskup3 · Accepted Answer

Your calculation for the mean is fine. But you can&#039;t just take a weighted average of standard deviations and expect to get the standard deviation for the population.You need the square root of the pooled variance.

Divide the population of U.S. workers into two categories: those who have a job in the goods-produci

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