A rowing club has a large number of members. A random sample of 12 of these members is taken and the pulse rate, \(x\) beats per minute (bpm), of each is measured after a 30 -minute training session. A \(98 \%\) confidence interval for the population mean pulse rate, \(\mu \mathrm{bpm}\), is calculated from the sample as \(64.22\lt \mu\lt 68.66\).
(a) Find the values of \(\sum x\) and \(\sum x^{2}\).
(b) State an assumption that is necessary for the confidence interval to be valid.