Question

A research team conducted a study showing that approximately 20% 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

Answer 1

The probabilities that the at least one tie is too tight is 0.878 and more than two ties are too tight is 0.323 and none are too tight is 0.122 and at least 18 are NOT too tight is 0.67.

According to the statement

We have given that the in a survey showing that the approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain.

And we have to find the probability on the some given conditions.

So, For this purpose, we know that the

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

Now,

A. Here n = 20, P = 0.1, And  X ≥ 1. Then

The probability that at least one tie is too tight P(≥ 1) = 1 - P(0)

P(≥ 1) = 1 - 0.12

P(≥ 1) = 0.878.

And

B. Here P(≤2) = 0.67 Then

The probability that more than two ties are too tight P(≥ 3) = 1 - P(≤2)

P(≥ 3) = 1 - 0.67

P(≥ 3) = 0.323

And

C. The probability that none are too tight P(0) = 0.122.

And

D. Here n =20, P = 0.1 and X≤2

The probability that at least 18 are NOT too tight P(X≤2) = 0.67.

So, The probabilities that the at least one tie is too tight is 0.878 and more than two ties are too tight is 0.323 and none are too tight is 0.122 and at least 18 are NOT too tight is 0.67.

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Question:

A research team conducted a study showing that approximately 20% 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

A. What is the probability that at least one tie is too tight?

B. What is the probability that more than two ties are too tight?

C. What is the probability that none are too tight?

D. What is the probability that at least 18 are NOT too tight?

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