Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable $$Y _ { 1 } + Y _ { 2 }$$ $$\begin{array} { c | c c }
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 150 & 12 \
\mathrm { Y } & 200 & 18
\end{array}$$
A)? = 350,? = 21.63
B)? = 350,? = 30
C)? = 400,? = 25.46
D)? = 400,? = 36
E)? = 400,? = 6.00

Question

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable $$Y _ { 1 } + Y _ { 2 }$$ $$\begin{array} { c | c c } 
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 150 & 12 \
\mathrm { Y } & 200 & 18
\end{array}$$
A)? = 350,? = 21.63
B)? = 350,? = 30
C)? = 400,? = 25.46
D)? = 400,? = 36
E)? = 400,? = 6.00

Quizplus · Accepted Answer

To find the mean of the variable, we add the means of the independent variables.

μ = 350 + 50 = 400

To find the standard deviation, we first use the formula for the variance of the sum of independent variables:

Var(X + Y) = Var(X) + Var(Y)

Then we take the square root to find the standard deviation:

σ = sqrt(σ_X^2 + σ_Y^2)

σ = sqrt(15^2 + 20^2) ≈ 25.46

Therefore, the correct answer is C.

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