Question

a research team conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral function. at a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities? at least one tie is too tight , more than two ties are too tight, no tie is too tight, at least 13 ties are not too tight

Answer 1

Let X be the number of businessman wearing ties too tight.

X~Binomial(15,0.1) distribution

PDF of a binomial (15,0.1) distribution is given as:

P(X=x) = 15Cx*0.1^x*0.9^15-x where x=0,1,2,,,15

Now, P(X>=1) = 1- P(X=0) = 1- 15C0*0.9^15 = 0.7941

P(X>2) = 1- P(X=0) - P(X=1) - P(X=2) = 0.1841

P(X=0) = 0.2059

P(X>=13) = P(X=13) + P(X=14) + P(X=15) is <0.000001 ie approximately 0