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 and if it dispenses less, customers may complain.

BIG Corporation would like to estimate the mean amount of coffee, I, 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 u. Assuming the standard deviation of cup amounts dispensed by this machine is 0.42 ounces, what is the minimum sample size needed in order for BIG to be 90% confident that it's estimate is within 0.05 ounces of u?

Carry your intermediate computations to at least 3 decimal places.

Write your answer as a whole number.