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Unformatted text preview: IE 111 Solutions 9:00 Section Exam 1.1 Fall 2007 9:00 Exam 1 30's 56 40's 344999 Ave= 66.25 50's 4589 Med= 68.5 60's 36 N= 28 70's 123689 SD= 18.4 80's 02278 90's 256 Question 1. Consider the Venn diagram and associated probabilities below: P(A) = 0.4 P(D)=0.1 P(B ∪ D)=0.35 P(A ∩ B) = 0.14 P(C) = 0.39 a) Find P(A ∪ B) P(B) = P(B ∪ D) = 0.35 because D is a proper subset of B P(A ∪ B) = P(A)+P(B) P(A ∩ B) = 0.4+0.350.14 = 0.61 b) Are A and B independent? Show why or why not. P(A)P(B) = 0.35*0.4 = 0.14 = P(A ∩ B) = 0.14 Therefore they are independent c) Find P(B) P(B) = P(B ∪ D) = 0.35 because D is a proper subset of B d) Find P(DB) P(DB) = P(D ∩ B)/P(B) = P(D)/P(B) = 0.1/0.35 = 0.285714 e) What is P(EA) P(EA) = 0 since E and A are mutually exclusive f) Are A and E independent? Show why or why not. P(A ∪ B ∪ C) = P((A ∪ B) ∪ C) = 0.61+0.31 = 1 Since E is M.E. from A, B, and C we have P(E)=0 Since P(EA)= P(E)=0, they are independent S A B C E D Question 2....
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 Spring '07
 Storer
 Type I and type II errors, TB P=0.00001 P=0.0000099, TB P=0.01 P=0.0000001, Med= N= SD=

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