Confidence interval: how to show that a given mean is plausible or not?

Question

I am going through some questions as practice for my STATS examination and I am baffled with one question pertaining confidence intervals. There are three parts to this question, I can do parts (a) and (b), however I am stuck with part (c). Below is the question: My solutions to parts (a) and (b) are as follows: Could somebody please assist me with (c) or at least explain what am I supposed to do? It would be highly appreciated. Thanks

Answer 1

When you construct a 95% confidence interval, it gives an interval with plausible values at 5%. To see whether the mean is plausible or not, you simply have to see whether the mean is in the interval. If the mean is in the interval, then it is a plausible value.