Final Answer:
H is not a binomial variable. To understand why, we need to look at what defines a binomial variable. A variable is binomial if it satisfies the given conditions.
Step-by-step explanation:
1. Fixed number of trials (n): The experiment consists of a fixed number of repeated trials or observations.
2. Each trial is independent: The outcome of any trial does not influence the outcome of another.
3. Each trial has only two possible outcomes: These outcomes are usually labeled as "success" and "failure."
4. The probability of success (p) is the same for each trial: The probability of getting a "success" does not change from trial to trial.
Now let's apply these criteria to the situation with Johann and his coworkers:
- Johann's sample does have a fixed number of trials, n=10, as he is asking exactly 10 coworkers about their hours.
- The hours worked by one coworker are assumed to be independent of the hours worked by another, so this condition is met.
- However, the number of hours worked by an individual is not a "success" or "failure" but is instead a numerical value that can vary widely. This means it is not simply a binary outcome and the scenario does not have two outcomes; hours worked is a continuous variable.
- Moreover, there cannot be a fixed probability of "success" because we do not have a binary outcome in this case.
Since conditions 3 and 4 are not met, h (the average number of hours worked) cannot be considered a binomial variable.
It is instead a continuous variable that could be better described by other distributions, such as the normal distribution if the sample size is large enough and the underlying conditions of the Central Limit Theorem are met.