A sprinkler system is being installed in a large office complex. Based on a series of test runs, a 99% confidence interval for the population mean $\mu$, the average activation time of the sprinkler system (in seconds), is found to be (22, 28). Determine whether each of the following statements is true or false.
a) The 99% confidence level implies that it is quite likely that the population mean is between 22 and 28.
b) The 99% confidence level implies that it is quite likely that the sample mean is between 22 and 28.
c) The 99% confidence level implies that 99% of the sample means obtained from repeated sampling would fall between 22 and 28.
d) If a 95% confidence interval were calculated from the same data, (23, 27) would be a possible interval.
I think I have gotten a,b and d but could someone help me understand why c is true/false?