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)
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