Aresearch team at cornell university 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 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:
a) at least 5 ties are too tight?
b) at most 12 ties are too tight?

a) The probability that at least 5 ties are too tight is P=0.0432.

b) The probability that at most 12 ties are too tight is P=1.

Step-by-step explanation:

In this problem, we could represent the proabilities of this events with the Binomial distirbution, with parameter p=0.1 and sample size n=20.

a) We can express the probability that at least 5 ties are too tight as:

The probability that at least 5 ties are too tight is P=0.0432.

a) We can express the probability that at most 12 ties are too tight as:

The probability that at most 12 ties are too tight is P=1.

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