document.write( "Question 393697: AT A COLLEGE, 1 OUT OF 4 STUDENTS ARE SOPHOMORES. IF 5 STUDENTS SURVEYED FIND THE
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Algebra.Com's Answer #279386 by ewatrrr(24785)\"\" \"About 
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document.write( "Hi
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document.write( "1 OUT OF 4 STUDENTS ARE SOPHOMORES
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document.write( "p(sophmore) = p = .25  P(not sophmore) = q = .75
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document.write( "5 STUDENTS SURVEYED FIND: 
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document.write( "A)MEAN = 5*.25
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document.write( "B) VARIANCE = 5*.25*.75
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document.write( "C)STANDARD DEVIATION = sqrt(5*.25*.75)\r
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document.write( "Note: The probability of x successes in n trials is: 
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document.write( "P = nCx* \"p%5Ex%2Aq%5E%28n-x%29\" where p and q are the probabilities of success and failure respectively. 
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document.write( "In this case p = .25 & q = .75
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document.write( "nCx = \"n%21%2F%28x%21%28n-x%21%29%29\"
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document.write( "D) PROBABILITY THAT EXACTLY 3 ARE SOPHOMORES = 10(.25)^3(.75)^2 = .0879
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document.write( "E)PROBABILITY THAT AT MOST 2 OR SOPHOMORES = P(0) + P(1) + P(2) 
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document.write( "P(0) + P(1) + P(2) =  .75^5 + 5*(.25)^1 *(.75)^4 + 10*(.25)^2 *(.75)^3 
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document.write( "P(0) + P(1) + P(2) = .2373 + .3955+ .2637 = .9844
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document.write( "F) AT LEAST 3 ARE SOPHOMORES = 1 -P(0) + P(1) + P(2) = .0156 \n" );
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