Find the required probability for binomial distribution.
Sociology: Dress Habits A research team at Cornell University conducted a study showing that around 10 percent of all businessmen who wear ties wear them so right that they actually decrease blood flow to the brain, diminishing cerebral functions (Source: Chances: Risk and Odds in Everyday Life, by James Burke). At a board meeting of 20 businessmen, all of whom wear ties, what is the probability that
1) At least one tie is too tight?
2) More than two ties are too tight?
3) None are too tight?
4) At least 18 are not too tight?