A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. BIG Corporation would like to estimate the mean amount of coffee,
\mu
, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate
\mu
. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.43 ounces, what is the minimum sample slize needed in order for B1G to be
99%
confident that its estimate is within 0.08 ounces of
\mu
?