Question

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

Answer 1

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%.

What is the binomial distribution formula?

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