8. Suppose that X and Y are means from two large (larger than 30) independent samples E(X)= 106; Var (X)= 16; E(Y)-98; Var(Y) =9. Based on the Central Limit Theorem, we can say that P(X-Y>10) is approximately: (A) 0.3446 (B) 0.2236 (C) 0.4681 (D) 0.3859 (E) 0.0228

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8. Suppose that X and Y are means from two large (larger than 30) independent samples
E(X)= 106; Var (X) = 16; E(Y) =98; Var(Y) = 9.
Based on the Central Limit Theorem, we can say that P(X-Y>10) is approximately:
(A) 0.3446
(B) 0.2236
(C) 0.4681
(D) 0.3859
(E) 0.0228
Transcribed Image Text:Answer is A 8. Suppose that X and Y are means from two large (larger than 30) independent samples E(X)= 106; Var (X) = 16; E(Y) =98; Var(Y) = 9. Based on the Central Limit Theorem, we can say that P(X-Y>10) is approximately: (A) 0.3446 (B) 0.2236 (C) 0.4681 (D) 0.3859 (E) 0.0228
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Can you explain why it is you added V(X-Y) = V(X) + V(Y) = 16 + 9 =25? What is the reasoning behind it? What if it was V(X+Y)? Would you then do the opposite and subtract

= V(X) - V(Y) = 16 - 9 = 7? 

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