A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed with a mean of 15 grams and standard deviation of 0.15 grams.
a. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. What is the standard deviation of the sampling distribution of the sample mean weight?
b. Suppose the inspectors sample 100 ravioli. How does the standard deviation of the sampling distribution of the sample mean change?
c. In which case is it more likely that they will see a sample mean weight of cheese filling less than 14.95 grams?