Sally is tracking her spending. Every day for n days, Sallytracks the exact amount of dollars he spends that day, which is anonnegative real number but not necessarily an integer. Forpositive integers i ≤ n, he spends xi dollars on day i. Forexample, on day 1, he spends x1 dollars. At the end of the n days,he calculates the average daily amount he spends on his food to beaveragex = (x1 + x2 + · · · + xn)/n.
a) Prove that on at least one of the n days, Jarett paid atleast averagex dollars.
(b) Prove that on fewer than half of the n days, Jarett paidstrictly more than 2averagex dollars.
