Suppose that 40 randomly selected squirrels were selected and weighed. The sample mean weight was found to be 12.5 grams. Assume that the population standard deviation is known to be 1.1 grams.

1. Someone computes the 99% confidence interval for the average weight of a Mexican free-tail bat as 12.5 2.576(1.1). What is the mistake of this student?

2. After correcting the mistake in part (1.1), the student states "I am 99% confident that the sample mean weight is between 12.052 and 12.948 grams." What is wrong with this statement?

3. The student quickly realizes the mistake made in part (1.2) and now says "The probability that the true mean weight is between 12.052 and 12.948 grams is 99%." What misinterpretation is the student making now?

4. Finally, to defend the use of the Normal distribution to calculate the confidence interval the student says, "Because the sample size is quite large, the population of weights will be approximately Normal." Correct this misunderstanding.