Decide whether the experiment is a binomial experiment. If it is, identify a suc

Question

Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment) explain why. A survey asks 1400 chief financial officers, "Has the economy forced you to postpone or reduce the amount of vacation you plan to take this year?" Thirty-one percent of those surveyed say they are postponing or reducing the amount of vacation. Twenty officers participating in the survey are randomly selected. The random variable represents the number of officers who are postponing or reducing the amount of vacation. (Source: Robert Half Management Resources)

Explanation / Answer

There are four assumptions regarding with Binomial distribution

1) sample size (n) is fixed here n = 20 chief financial officers are randomly selected so this assumption satisfy

2)Each replication of the process results in one of two possible outcomes (success or failure),

here possible outcomes are 1) postpone vacation plan or reduce the amount of vacation plan and 2) not postpone vacation plan and not reduce the amount of vacation plan.

That is we have success and failure types of outcomes and this assumption also satisfied.

3)The probability of success is the same that is constant for each replication, and

Here proportion of postponding or reducing the amount of vocation is 31% so p = 0.31 is constant and this assumption also satisfied.

4) The replications(that is trials) are independent,

here that a success in one respondent does not influence the probability of success in another respondent.

That is their responses are independents

So all the assumption are valid and we can use Binomial distribution.

So the experiment is a binomial experiment.

Let X be a random variable which takes the value of the number of officers who are postponing or reducing the amount of vacation.

There are 20 random variables so values of X from 0 to 20

X may takes any value from 0 to 20

That is X belongs to { 0, 1, 2, ....20}

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