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 σ 2 = 8 ounces. experiments are conducted using both machines with sample sizes of 81 each. the sample averages for machines a and b are x¯ a = 7.4 ounces and x¯ b = 7.5 ounces. engineers are surprised that the two sample averages for the filling machines are different.(a) use the central limit theorem to determinep(x^b−x^a≥0.2)under the condition that μa=μb.(b) do the aforementioned experiments seem to, in anyway, strongly support a conjecture that the populationmeans for the two machines are different? explain using your answer in (a).