Final answer:
All of the choices above are correct since each statement can be valid within the context of a normal distribution with the given mean and standard deviation.
Step-by-step explanation:
To determine the validity of the choices, we consider the provided information about the weight loss distribution.
According to the information, we have a normal distribution with a mean weight loss of 12 pounds and a standard deviation of 3 pounds. Choice A states that one fourth of the members lost exactly two pounds, which is plausible if we are considering a diverse range of weight-loss outcomes.
Choice B describes the middle 50%, or the interquartile range, indicating that members lost between two to 8.5 lbs. This is also reasonable because, in a normal distribution, about 50% of values fall within roughly one standard deviation of the mean.
For Choice C, which indicates that most people lost between 3.5 and 4.5 lbs, this might represent the mode or the most frequently occurring value range in the data set, which is also possible within a normal distribution.