Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable Y - 19.Round to two decimal places if necessary. $$\begin{array} { l | l l }
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 300 & 29 \
\mathrm { Y } & 220 & 30
\end{array}$$
A)? = 201,? = 35.51
B)? = 201,? = 11
C)? = 201,? = 23.22
D)? = 220,? = 30
E)? = 201,? = 30

Question

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable Y - 19.Round to two decimal places if necessary. $$\begin{array} { l | l l } 
& \text { Mean } & \text { SD } \
\hline \mathrm { X } & 300 & 29 \
\mathrm { Y } & 220 & 30
\end{array}$$
A)? = 201,? = 35.51
B)? = 201,? = 11
C)? = 201,? = 23.22
D)? = 220,? = 30
E)? = 201,? = 30

Quizplus · Accepted Answer

If Y = X - 19, then E(Y) = E(X) - 19 and Var(Y) = Var(X).

So, the mean of Y is the same as the mean of X, which is μ = 201.

The standard deviation of Y is given by:

σ(Y) = sqrt(Var(Y)) = sqrt(Var(X)) = sqrt(30^2 + 11^2) ≈ 32.85 ≈ 30 (rounded to two decimal places).

Therefore, the best choice is E.

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