Question

17. (4 pts) A study found that approximately 10% of all businessmen who wear ties wear them so tight they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what is the probability that at least one tie is too tight?

Answer 1

Here, n = 20, p = 0.1, (1 - p) = 0.9 and x = 0
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

probability that none ties too tight
P(X = 0) = 20C0 * 0.1^0 * 0.9^20
P(X = 0) = 0.1216

required proability = P(X > 0) = 1 - 0.1216 = 0.8784