Applying Linear Functions to a Random Sequence

Question

3 points possible (graded)
Let (Zn)n≥1 be a sequence of random variables such that

n−−√(Zn−θ)−→−−n→∞(d)Z

for some θ∈R and some random variable Z.

Let g(x)=5x and define another sequence by Yn=g(Zn).

The sequence n−−√(Yn−g(θ)) converges. In terms of Z, what random variable does it converge to?

n−−√(Yn−g(θ))−→−−n→∞(d)Y.
(Answer in terms of Z)

Y=