Question

9. An item needs to go through 100 different independent processing until completion. Each process- ing takes exponential with a mean of 3 minutes. Approximately, what is the probability that the item will be finished in 8 hours? (Hint: Use the central limit theorem.)

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Answer #1

TOPIC:Application of Central limit theorem through Exponential distribution.

Now, im this rab tem ae have, Xi Finis hing time prab lem, we have t the cs den, i 1,2,--)00 H , X: ,亼 are iid Ext (w; tn mean=0.05 e ne variables. E 3 mintes yandom hours jdon, i 1,2,-,100. 0.05 hours lo o isa X; otal time to dimish. l00 100 aud, var var (x.) · 「Co variance teams vanish, due to independaxe 0.05 :놔 .05. O. 5 γ-E (Y)Now, we need din v0.25 JD-25 |소0000 oAma

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