Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable X - Y.Round to two decimal places if necessary. $$\begin{array} { l | l l }
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 220 & 16 \
\mathrm { Y } & 260 & 12
\end{array}$$
A)? = -40,? = 28
B)? = 480,? = 20.00
C)? = -40,? = 20.00
D)? = -40,? = 10.58
E)? = -40,? = 4

Question

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable X - Y.Round to two decimal places if necessary. $$\begin{array} { l | l l } 
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 220 & 16 \
\mathrm { Y } & 260 & 12
\end{array}$$
A)? = -40,? = 28
B)? = 480,? = 20.00
C)? = -40,? = 20.00
D)? = -40,? = 10.58
E)? = -40,? = 4

Quizplus · Accepted Answer

The mean of X-Y is the difference of the means: μX-μY = (60)-(-100) = 160
The standard deviation of X-Y is the square root of the sum of the variances: sqrt((σX)^2 + (σY)^2) = sqrt((400)+(400)) = 20. 
Therefore, the mean is 160 and the standard deviation is 20.00, rounded to two decimal places, which corresponds to answer choice C.

Given Independent Random Variables with Means and Standard Deviations as Shown,find