04exS - " BUT NOT "the maximum...

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ISOM111 Business Statistics (Fall 2010) Suggested Solutions for Tutorial Exercise 4 Please note that the tutorial exercise solutions may not be complete answers. Answers without showing the work in exam may earn you only partial credit. 1. X N (10 , 5 2 ) (a) P (10 6 X 6 12) = P μ 10 10 5 6 Z 6 12 10 5 = P (0 6 Z 6 0 . 4) =0 . 1554 (b) P ( X > 14 . 2) = P μ Z > 14 . 2 10 5 = P ( Z > 0 . 84) =0 . 5 0 . 2995 = 0 . 2005 (c) P (5 6 X 6 12 . 5) = P μ 5 10 5 6 Z 6 12 . 5 10 5 = P ( 1 6 Z 6 0 . 5) =0 . 3413 + 0 . 1915 = 0 . 5328 (d) P (4 6 X 6 14) = P μ 4 10 5 6 Z 6 14 10 5 = P ( 1 . 2 6 Z 6 0 . 8) =0 . 3849 + 0 . 2881 = 0 . 6730 1
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2. Let X be the monthly income of f ve-person families, X N (25 , 000 , 4000 2 ) (a) P (24000 <x< 30000) = P ( 24000 25000 4000 < x 25000 4000 < 30000 25000 4000 ) = P ( 0 . 25 <z< 1 . 25) = P ( 0 . 25 <z< 0) + P (0 <z< 1 . 25) =0 . 0987 + 0 . 3944 =0 . 4931(49 . 31%) (b) Let x a betheincomelim itfor f ve-person families so that the percentage of eligible families is at most 10% P ( x<x a )=0 . 1 P ( z< x a 25000 4000 )=0 . 1 P ( z<z a )=0 . 1 z a = 1 . 29 The limit: $25000 1 . 29($4000) = $19840 PLEASE NOTE that if the question here asked "the maximum income limit for f ve-person families so that the
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Unformatted text preview: &quot; BUT NOT &quot;the maximum income limit for f ve-person families so that the percentage of eligible families is at most 10% &quot;, then the z score here will be − 1 . 28 (the closest z with tail area is about 10%) and the answer is $19880 (c) Proportion of eligible families P ( x &lt; 14400) = P ( z &lt; 14400 − 25000 4000 ) = P ( z &lt; − 2 . 65) = 0 . 5 − . 496 = 0 . 004 (d) Let the number of eligible families be Y and Y ∼ Bin (50 , . 004) P ( y &gt; 2) = 1 − P ( y = 0) − P ( y = 1) − P ( y = 2) = 1 − C 50 . 004 (1 − . 004) 50 − C 50 1 . 004 1 (1 − . 004) 49 − C 50 2 . 004 2 (1 − . 004) 48 = 1 − . 818402 − . 164338 − . 01617 = 0 . 00109 2 3. a) . 0107422 b) i) P ( x &gt; 30) = 0 . 99995 ii) P (46 ≤ x ≤ 52) = 0 . 5074 3...
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04exS - &amp;amp;quot; BUT NOT &amp;amp;quot;the maximum...

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