Answer:
x ≥ 117
Step-by-step explanation:
Let suppose Pₙ denoted the structural damage that is probable with n cans
Pₙ = P {X₁+ ....... + Xₙ ≥ w}
= P {X₁+ ....... + Xₙ-w ≥ 0 }
So weight of the ith can denoted by Xi
From CLT , ΣXi is normal with 3n and variance 0.09
w is independent of Xi and normal
So
ΣXi-w is also normal
then mean and variance are
E [ ΣXi - w] = 3n -400
Var (ΣXi-w) = var (ΣXi) +Var (w)
= 0.09n +1600
So Pₙ = P{ X₁ +X₂ +.... +Xₙ -w-(3n-400) /underroot 0.09n +1600 ≥ -(3n-400)/ understoot (0.09n +160v)
this can be simplified to≈ P₀ { Z ≥ 400 - 3n / undersoot (0.09n+1600)}
P{Z ≥ 1.28 } ≈ .1
on simplifying x ≥ 117
