The incomes in a certain large population of electricians have a Normal distribu

Question

The incomes in a certain large population of electricians have a Normal distribution with mean $60,000 and standard deviation $8000. Four electricians are selected at random from this population to be shipped to another region.

A. The distribution of the mean, x-bar, is Normal with mean $30,000 and standard deviation $8000.

B.The distribution of the mean, x-bar, is Normal with mean $15,000 and standard deviation $8000

C.The distribution of the mean, x-bar, is Normal with mean $60,000 and standard deviation $2,000.

DThe distribution of the mean, x-bar, is Normal with mean $60,000 and standard deviation $4000.

Explanation / Answer

Solution:- option D. The distribution of the mean, x-bar, is Normal with mean $60,000 and standard deviation $4000.

Explanation:-  

=> The mean of a sample (x-bar) is equal to the mean of the population (µ)

=> standard deviation = /sqrt(n) = $8000./sqrt(4) = $8000 / 2 = $4000.

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