A premium golf ball production line must produce all of its balls to 1.615 ounces in order to get the top rating (and therefore the top dollar). Samples are drawn hourly and checked. If the production line gets out of sync (i.e. the mean weight of the balls produced changes from 1.615 ounces) with a statistical significance of 5%, it must be shut down and repaired. Past experience indicates that a reasonable value for the standard deviation of weight is 0.03 ounces. The manufacturer wants to guarantee that a change of 0.01 ounces should be detected with more than 95% probability. Find out the minimum number of balls that must be sampled each time to satisfy this requirement. If you are using an approximation, clearly indicate where you are approximating the exact solution.