Two different box-filling machines are used to fill cereal boxes on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is σ2 = 1 ounce.

Experiments are conducted using both machines with sample sizes of 36 each. The sample averages for machines A and B are ¯xA = 4.5 ounces and ¯xB = 4.7 ounces. Engineers are surprised that the two sample averages for the filling machines are so different.

(a) Use the Central Limit Theorem to determine P(X¯B − X¯A ≥ 0.2)

under the condition that μA = μB.

(b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different?

Explain using your answer in (a).