(a)[4]
Amy recorded her resting pulse rate, $x$ beats per minute, at the same time each day for $30$ days. The data are summarised below. $\sum (x - 80) = -147$ and $\sum (x - 80)^2 = 952$. Determine the mean and standard deviation of Amy’s pulse rate.
(b)[3]
Amy’s friend Marok recorded her pulse rate each day after running for half an hour. Marok’s pulse rate, in beats per minute, was found to have a mean of $148.6$ and a standard deviation of $18.5$. Assuming that pulse rates are normally distributed, find the proportion of Marok’s pulse rates, after running for half an hour, that were above $160$ beats per minute.