Quiz 4 Key - Quiz4 (4/20/2010) n=10, p=1/2 1. (a) P (3 X A...

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Unformatted text preview: Quiz4 (4/20/2010) n=10, p=1/2 1. (a) P (3 X A 5) = P ( X = 3) + P ( X = 4) + P ( X = 5) 10 10 10 = 2)3 (1/ 2)7 + 2) 4 (1/ 2)6 + 2)5 (1/ 2)5 (1/ (1/ (1/ 3 4 5 = .1171 + .2051 + .2461 = .5683 (b) X ~ Bin(10,1/ 2) If n is large, X ~ Normal (np, ( np (1 - p )) 2 ) X ~ Normal (5,1.582 ) Without continuity correction, 3-5 5-5 <Z < ) = P (-1.27 < Z < 0) = 0.5 - P ( Z < -1.27) 1.58 1.58 = 0.5 - (1 - P ( Z < 1.27)) = 0.5 - 0.102 = 0.398 P (3 X & 5) P( (c) X ~ Bin(10,1/ 2) If n is large, X ~ Normal (np, ( np(1 - p )) 2 ) X ~ Normal (5,1.582 ) With continuity correction, (correction number = .5) 2.5 - 5 5.5 - 5 <Z < ) = P (-1.58 < Z < 0.31) 1.58 1.58 = P ( Z < .31) - P ( Z < -1.58) = P ( Z < .31) - (1 - P ( Z < 1.58)) = 0.6217 - (1 - 0.9429) = 0.5646 P (3 X 5) P (2.5 < X < 5.5) = P ( ...
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This note was uploaded on 03/28/2011 for the course AMS 110 taught by Professor N/a during the Spring '08 term at SUNY Stony Brook.

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