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valkas [14]
2 years ago
7

A questionnaire asks shareholders of a company to state whether they consider the

Mathematics
1 answer:
Oduvanchick [21]2 years ago
7 0

Using the binomial distribution, it is found that the probabilities are given as follows:

a) 0.5514 = 55.14%.

b) 0.3631 = 36.31%.

c) 0.4082 = 40.82%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

Item a:

In this problem, we have p = 0.82, n = 3, and the probability is P(X = 3), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.82)^{3}.(0.18)^{0} = 0.5514

Item b:

In this problem, we have p = 0.82, n = 3, and the probability is P(X = 2), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{3,2}.(0.82)^{2}.(0.18)^{1} = 0.3631

Item c:

We have to find P(X = 2) for the three probabilities, p = 0.82, p = 0.12, p = 0.05 and add them, hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{3,2}.(0.82)^{2}.(0.18)^{1} = 0.3631

P(X = 2) = C_{3,2}.(0.12)^{2}.(0.88)^{1} = 0.0380

P(X = 2) = C_{3,2}.(0.05)^{2}.(0.95)^{1} = 0.0071

Then:

p = 0.3631 + 0.0380 + 0.0071 = 0.4082.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

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