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Question 3 [16 marks] The average particulate concentration, in micrograms per cubic meter, was measured in a petrochemical complex at 36 randomly chosen times, with the following concentrations resulting: 5, 18, 15, 77, 133, 220, 130, 85, 103, 125, 80, 107, 124, 106, 113, 165, 137, 125, 124, 65, 82, 95, 77, 115, 70, 110, 144, 128, 133, 81, 129, 114, 45, 92, 117, 153 a) Represent the data in a histogram. b) [l mark] Is the histogram approximately normal? c) Calculate the sample mean X d) Calculate the sample standard deviation S. e) Determine the proportion of the data values that lies within X ± 1.55 and compare with the lower bound given by Chebyshevs inequality f Determine the proportion of the data values that lies within X t 2S and compare with the lower bound given by Chebyshevs inequality.

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