A federal inspector for weights and measures visits a packaging plant to affirm

Question

A federal inspector for weights and measures visits a packaging plant to affirm that the net weight of packages is as indicated on the packages. The plant manager assures the inspector that the packaging process results in an average weight of 680 grams and a standard deviation of 18 grams. The inspector selects 200 packages at random and finds their average weight to be 678.4 grams.

a. Specify the sampling distribution of the average weight of 200 packages randomly selected (assuming the manager’s statement is accurate).

b. If the manager’s statement is accurate, how likely is a sample mean of 678.4 grams or less?

c. Based on your result in part b, does the inspector have convincing evidence that the process is underfilling packages, on average? Explain your answer.

Explanation / Answer

a)from central limit theorum sampling distribution of the average weight of 200 packages randomly selected will be approximately normal with mean =680

and std error of them mean =std deviation/(n)1/2 =1.273

b) P(X<678.4)=P(Z<(678.4-680)/1.273)=P(Z<-1.2569)=0.1044

c)No as above probability is greater then 0.05; we can not claim that to be unusal.

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