Z1,Z2,.... are identically independently distributed with uniform distribution [-20,10]. How do i use the central limit theorem to estimate the the probability

P(summation (900, i=1) : Zi >= -4470)

My attempt

E(Zi)=-5

Var(Zi)=80

P(summation Zi <= -4470) = P([summation Zi]/900 <= [-4470]/900)

=P(sample Z (900) <= 80)

=P([sample Z (900) + 5]/sqrt(80/900) <= [80+5]/sqrt(80/900))

~=P(Z<=285.1) where Z~Normal(0,1)