The purpose of the quality control sampling of the Widget production lines is to determine whether the lines are malfunctioning or not. Namely, if the mean length of the sample is too different from the population mean of 24 cm and population s = 0.20 cm, maintenance will shut down the production line that was sampled.
Question: Using the population s, determine how large the sample size has to be in order for the sample mean to be determined at the 0.01 significance level, while having an acceptable sampling error of e = 0.02 cm.