SOLUTION: A research team conducted a study showing that approximately 25% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishin

Question 1134538: A research team conducted a study showing that approximately 25% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)
(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 18 ties are not too tight

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
at least one tie is 1-(no ties)
P(no tie too tight) is 0.75^20=0.0032 so 1-0.0032 is 0.997
for 1 tie it is 20*.25*.75^19=0.0211
for 2 ties it is 20C2*.0.25^2*0.75^18=0.0669
sum of those three is 0.0922, so more than two is the complement or 0.9078 or 0.908.
no tie is too tight is 0.0032 from above
at least 18 are not too tight means 18, 19, 20 aren't too tight, and that means that 2, 1,0 are too tight, and that is 0.0922
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