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Alan is a facility manager who carried out a study about the monthly electricity bill (in HK$100) of the shop. He then randomly selected previous 48 months' data for analysis and listed as follows. 2.34 4.11 5.5 5.3 5.99 4.07 4.05 6.11 2.71 5.59 6.55 10.07 + 0.1 x T 1.46 6.79 2.95 0.01 7.49 6.59 7.36 3.79 3.64 6.73 6.61 10.08 + 0.1 x U 7.99 9.2 6.35 5.99 9.57 8.51 8.32 4.01 5.03 6.28 12.01 10.09 + 0.1 x S 7.6 5.93 8.93 8.56 7.64 8.26 8.07 6.44 9.73 6.42 9.11 10.06 + 0.1 x R Suppose a frequency table is constructed using 6 classes. Use the smallest data value from the above sample as the lower class limit of the first class. (a) Find the class width and complete the frequency table in your answer script. (12 marks) (b) Estimate the mean and the variance based on the frequency table constructed in part (a). Correct your final answers to 3 decimal places. (4 marks) ( c) Suppose at least 84% of the monthly electricity bills are within the interval (in HK$100) from X to Y. By using the Chebyshev's theorem, find the interval (in HK$100) from X to Y of the monthly electricity bill around the mean. Correct your final answers to 3 decimal places. (4 marks)