Two different box-filling machines are used 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=3 ounces. Experiments are conducted using both machines with sample sizes of 81 each. The sample averages for machines A and B are xˉA​=12.2 ounces and xˉB​=12.4 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Use the Central Limit Theorem to determine P(XB​−XA​≥0.2) under the condition that μA​=μB​. P(XB​−XA​≥0.2)= (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). Since the probability in (a) negligible, the experiments support the conjecture.