Question

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).

Answer 1

Answer:

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.