An operator of a filling machine plotted the weights of each bag she filled for three weeks. At the same time, a quality inspector randomly took groups of five bags of the same output and plotted the average weights of the samples. The inspector's sampling distribution will
A) show if the output has been produced to the operator's specifications.
B) have greater variability than the operator's distribution.
C) have a mean five times greater than the operator's distribution.
D) have less variability than the operator's distribution.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will have less variability than the distribution of individual weights due to the Central Limit Theorem, which states that the standard deviation of the sampling distribution is the population standard deviation divided by the square root of the sample size.

An Operator of a Filling Machine Plotted the Weights of Each