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; if it dispenses less, the customers may complain.

BIG Corporation would like to estimate the mean amount of coffee,, 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 . Assuming that the standard deviation of cup amounts dispensed by this machine is 0.40 ounces, what is the minimum sample size needed in order for BIG to be 95% confident that its estimate is within 0.06 ounces of ?

Round up to at least three decimal places. Write the answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).