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).

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when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

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