The admissions director for a university found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct, based on that information.

a. There is a 95% probability that the interval from 107.8 to 116.2 contains μ.

b. There is a 95% chance that the interval (107.8, 116.2) contains x̅.

c. This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples.

d. If we take many samples, about 95% of them will contain the interval (107.8, 116.2).

e. The probability that the interval (107.8, 116.2) captures μ is either 0 or 1, but we don’t know which.