- #1

Harmony

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1) Find the probability that 5 large loaves of bread are heavier than 10 small loaves.

My Working:

Let X be the weight of a large loaf, Y be the weight of a small loaf

X~N(420, 900) , Y~N(220,100)

5X>10Y

5X-10Y>0

X-2Y>0

E(X-2Y)=E(X) - 2E(Y)=420-440=-20

Var(X-2Y)=Var(X)+4Var(Y)=900+400=1300

P(X-2Y>0)=P(Z>20/(1300)^1/2)=P(Z>0.5547)=0.2896

But the answer given is totally different. Is there anything I miss in my working?