Explaining confidence The admissions director from Big City 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.

(a) There is a 95% probability that the interval from 107.8 to 116.2 contains m.

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

(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 m is either 0 or 1, but we don’t know which.