Question

A survey asks 1200 ​workers, "Has the economy forced you to reduce the amount of vacation you plan to take this​ year?" Forty​-six percent of those surveyed say they are reducing the amount of vacation. Twenty workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. 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. Is the experiment a binomial​ experiment?

Answer 1

Answer:

It is a binomial experiment.

A success is a worker saying that the economy forced him to reduce the amount of vacation you plan to take this​ year.

$n = 20$

$p = 0.46$

$q = 0.54$

The random variable x can assume any value from 0 to 20, inclusive.

Explanation:

For the question that is asked to the workers( "Has the economy forced you to reduce the amount of vacation you plan to take this​ year?") there are two possible answers, only two possible outcomes. So yes, it 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.

A success is a worker saying that the economy forced him to reduce the amount of vacation you plan to take this​ year.

n is the amount of workers that participate in the survey. So $n = 20$

p is the decimal probability of a success. Forty​-six percent of those surveyed say they are reducing the amount of vacation. So $p = 0.46$

q is the decimal probability of a failure. The sum of the probability of a failure and a success must be decimal 1. So

$p + q = 1$

$0.46 + q = 1$

$q = 0.54$

The values of the random variable x are the number of workers that say they are reducing their amount of vacation. 20 workers are surveyed, so the random variable x can assume any value from 0 to 20, inclusive.