IE4521_HW4_Solution

IE4521_HW4_Solution - Solution 4 IE4521 Fall 2009, October...

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Solution 4 IE4521 Fall 2009, October 20. 1. ( 5.3.2) (a) The exact probability is ( 10 7 ) 0 . 3 7 0 . 7 3 + ( 10 8 ) 0 . 3 8 0 . 7 2 + ( 10 9 ) 0 . 3 9 0 . 7 + 0 . 3 10 = 0 . 0106 The normal approximation is 1 - Φ( 7 - 0 . 5 - (10 × 0 . 3) 10 × 0 . 3 × 0 . 7 ) = 0 . 0078 . (b) The exact probability is ( 21 9 ) 0 . 5 21 + ( 21 10 ) 0 . 5 21 + ( 21 11 ) 0 . 5 21 + ( 21 12 ) 0 . 5 21 = 0 . 6167 The normal approximation is Φ( 12 + 0 . 5 - (21 × 0 . 5) 21 × 0 . 5 × 0 . 5 ) - Φ( 8 + 0 . 5 - (21 × 0 . 5) 21 × 0 . 5 × 0 . 5 ) = 0 . 6156 . (c) The exact probability is ( 7 0 ) 0 . 8 7 + ( 7 1 ) 0 . 20 . 8 6 + ( 7 2 ) 0 . 2 2 0 . 8 5 + ( 7 3 ) 0 . 2 3 0 . 8 4 = 0 . 967 The normal approximation is Φ( 3 + 0 . 5 - (7 × 0 . 2) × 0 . 2 × 0 . 8 ) = 0 . 9761 . 1
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(d) The exact probability is ( 12 9 ) 0 . 65 9 0 . 35 3 + ( 12 10 ) 0 . 65 10 0 . 35 2 + ( 12 11 ) 0 . 65 11 0 . 35 = 0 . 3410 The normal approximation is Φ( 11 + 0 . 5 - (12 × 0 . 65) 12 × 0 . 65 × 0 . 35 ) - Φ( 8 + 0 . 5 - (12 × 0 . 65) 12 × 0 . 65 × 0 . 35 ) = 0 . 3233 2. (5.3.11) The expectation of the strength of a chemical solution is
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IE4521_HW4_Solution - Solution 4 IE4521 Fall 2009, October...

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