hw2_sol

# hw2_sol - ORIE 4580/5580/5581 Solutions for Homework...

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ORIE 4580/5580/5581 Solutions for Homework Assignment 2 Question 1 a) Let D be the total customer demand in a month. Since sum of independent normally distributed random variables is normally distributed, D N (20 × 60 , 20 × 20 2 ) N (1200 , 8000) We want to ﬁnd s such that P { D s } ≥ 0 . 95 . Thus, we need to ﬁnd s such that P { D - 1200 8000 s - 1200 8000 } 0 . 95 = P { N (0 , 1) s - 1200 8000 } 0 . 95 . From the standard normal distribution tables, P { N (0 , 1) 1 . 64 } ≈ 0 . 95 . (Or one can use =NORMINV(0.95,0,1) function in Excel.) Therefore, s - 1200 8000 1 . 64 = s 1200 + 8000 × 1 . 64 1347 . 12 . s should be 1347 . 12. b) Let D 1 and D 2 be the demand that has to be satisﬁed from the ﬁrst and second tank. Since sum of independent normally distributed random variables is normally distributed, D 1 N (15 × 60 , 15 × 20 2 ) N (900 , 6000) , D 2 N (5 × 60 , 5 × 20 2 ) N (300 , 2000) .

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hw2_sol - ORIE 4580/5580/5581 Solutions for Homework...

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