Hello! As we don't know the number of patients, to solve this exercise, we have to analyze all the sentences and find the most correct:
• Last month more than half of their patients lost at least 6 pounds.
Let's imagine that she has 4 patients, with the corresponding loss:
2, 3, 5, 14 = a total of 24 pounds, but only one patient lost at least 6 pounds (and not half of them).
False.
• Two months ago at least one of their patients lost at least 6 pounds.
False, because we're talking about last month, and don't about two months ago.
• Last month at least one of their patients lost more than 3 pounds.
True. To keep the mean equal to 6, at least one of the patients needs to lose more than 3 pounds, like the example: 5 patients, with losses:
1 + 1 + 2 + 2 + 24 = 30 pounds (mean 6 pounds). In this case, three girls lost less than 3 pounds in just 1 loss more than that.
• Last month some of their patients lost at least 6 pounds.
True. As the example in the third alternative,
• Last month some of their patients lost exactly 6 pounds.
False. As we're talking about the mean, we don't need to expect that the losses will be exactly the same as the mean.
• Or none of the above statements are true.