Final answer:
In this exercise, the fitness center is interested in determining the mean amount of time a client exercises in the center each week. The population is all the clients of the fitness center, while the sample is a group of clients selected from the population. The parameter and statistic are the mean amount of time a client exercises in the center each week for the population and sample, respectively.
Step-by-step explanation:
The population in this exercise is all the clients of the fitness center. The sample is a group of clients selected from the population. The parameter is the mean amount of time a client exercises in the center each week for the entire population. The statistic is the mean amount of time a client exercises in the center each week for the sample. The variable is the amount of time a client exercises in the center each week. The data is the recorded times of exercise for each client in the sample.
In this exercise, the shape of the data is not provided, so it is not possible to determine whether part a or c of the question gives a more appropriate result. However, if the data is normally distributed, then the most appropriate measure of center would be the mean.
The question is not asking for proportion or technology-related parameters, so option b and c are not applicable in this exercise.