Mathematics: Let x denote daily work hours. suppose that for the sample of workers you have, the average daily work hours are 8 hours, with a standard deviation of 5. suppose now let z denote weekly work hours, find the mean and standard deviation for z (assuming everyone works 5 days per week in your sample).

123/100Step-by-step explanation:...

Let x denote daily work hours. suppose that for the

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15.01.2022

The mean for Z is 40.

The standard deviation for Z is 25.

Step-by-step explanation:

We are given the following in the question:

X: daily work hours.

The average daily work hours are 8 hours, with a standard deviation of 5.

$E(x) = 8\\S.D(X) = 5$

Var(X) = 5^2 = 25

Z denote weekly work hours.

We have to find the mean and standard deviation for Z.

$E(Z) =E(5x) = 5\tims E(X) = 5\times 8 = 40$

The mean for Z is 40.

We use the property:

Var(ax) = a^2Var(x)

$Var(Z) = Var(5x) = 5^2(Var(X)) = 25\times 25 = 625\\S.D(Z) = \sqrt{625} = 25$

Thus, the standard deviation for Z is 25.

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