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) have greater variability than the operator's distribution.
B) have less variability than the operator's distribution.
C) show if the output has been produced to the operator's specifications.
D) have a mean five times greater than the operator's distribution.

Question

Quizplus · Accepted Answer

The quality inspector's sampling distribution will have less variability than the operator's distribution because the inspector is averaging groups of bags, which reduces random variation. This is a common feature of sampling distributions, where the variability decreases as the sample size increases. Option A is incorrect because the sampling distribution has less variability. Option C is not specific to the question because the sampling distribution only shows the average weight, not if it has been produced to the operator's specifications. Option D is incorrect because the mean of the sampling distribution will be equal to the mean of the operator's distribution.

An Operator of a Filling Machine Plotted the Weights of Each