Problem

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, $\mu$ bpm, is calculated from the sample as $64.22 < \mu < 68.66$.

(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.