Question

A survey asks workers, "has the economy forced you to reduce the amount of vacation you plan to take this year?" Forty-three percent of those surveyed say they are reducing the amount of vacation. Thirty 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

This is a binomial experiment where each of the 30 trials (n) has two outcomes: reducing vacation or not (success is reducing vacation). The probability of success (p) is 0.43, and the probability of failure (q) is 0.57. The random variable (x) can take on values from 0 to 30.

Step-by-step explanation:

The scenario presented is indeed a binomial experiment. We meet the three required criteria for a binomial experiment: a fixed number of trials, two possible outcomes for each trial, and independent trials with the same probability of success.

A "success" in this context is defined as a worker who is reducing the amount of vacation due to the economy. The number of trials (n) is 30 (the number of workers surveyed). The probability of success (p) is 0.43 as 43% of the surveyed workers are reducing vacation time. Consequently, the probability of failure (q) is 1 - p, which equals 0.57.

The possible values of the random variable (x), which represents the number of workers who are reducing their vacation time out of the 30 selected, range from 0 to 30. This is because x can be any integer value within the number of trials (n).