A survey asks 1500 workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?" Fifty-ninenine 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.

Question

Social Studies

Nathaly Choi

20 November, 08:40

A survey asks 1500 workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?" Fifty-ninenine 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.

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Nia French · Answer 1

Given that X is a random variable representing the number of workers who are reducing the amount of vacation.

Here each worker is independent of the other.

And also there are only two outcomes yes or no.

So X is binomial

Success is the random worker saying they are reducing the amount of vacation.

p = Probability for a random worker who say they are reducing the amount of vacation.

=59% = 0.59

n=20 (no of workers surveyed)

X can take values as 0,1,2 ... 20

(since sample size = 20)