A research team conducted a study showing that approximately

A research team conducted a study showing that approximately 15% 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 15 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 13 ties are not too tight

Solution

a)Pr No ties are too tight=(.85)^15. Pr[At least 1 too tight]=1-(.85)^15=.9126
b)1-summation[15Ck(.15^k)(.85)^15-k] k=3 to k=15=1-.604225=.395775
c)(.85)^15=.087354219
d)1-.39569=.60431
.2856 .2312 .08735=.604