Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 4X + 19.Round to two decimal places if necessary. $$\begin{array} { l | l l }
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 100 & 14 \
\mathrm { Y } & 120 & 7
\end{array}$$
A)? = 400,? = 75
B)? = 419,? = 75
C)? = 400,? = 56
D)? = 419,? = 59.14
E)? = 419,? = 56

Question

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 4X + 19.Round to two decimal places if necessary. $$\begin{array} { l | l l } 
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 100 & 14 \
\mathrm { Y } & 120 & 7
\end{array}$$
A)? = 400,? = 75
B)? = 419,? = 75
C)? = 400,? = 56
D)? = 419,? = 59.14
E)? = 419,? = 56

Quizplus · Accepted Answer

The mean of 4X + 19 is 4 times the mean of X plus 19, which is 4(100) + 19 = 419. The standard deviation of 4X is 4 times the standard deviation of X, which is 4(14) = 56.

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