A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tight 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 is the probability that:
(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?
The binomial distribution will be used. Answers may vary slightly depending on whether the binomial distribution formula, the binomial distribution table, or distribution results from a calculator or computer are used. Please answer the following questions and then complete the problem: What makes up a trial? What is a success? What is a failure? What are the values of n, p, and q?