If the random variable X has mean 3 and standard deviation 5 , then...

Given the standard deviation of $X$ is $5$.

The variance of $X$ is $Var(X) = 5^2 = 25$.

Using the property of variance, $Var(aX + b) = a^2 Var(X)$.

For the random variable $Y = 2X - 5$, we have $a = 2$ and $b = -5$.

Var(Y) = 2^2 Var(X) = 4 \times 25 = 100$.<br><br>Answer:$100