Problem 1: A sample of 77 individuals working at a particular office was selected and the noise level (dBA) experienced by each individual was determined, yielding the following data ("Acceptable Noise Levels for Construction Site Offices." Building Serv. Engr. Research and Technology, 2009: 87-94). 55.3 55.3 55.3 55.9 55.9 55.9 55.9 56.1 56.1 56.1 56.1 56.1 56.1 56.8 56.8 57.0 57.0 57.0 57.8 57.8 57.8 57.9 57.9 57.9 58.8 58.8 58.8 59.8 59.8 59.8 62.2 62.2 63.8 63.8 63.8 63.9 63.9 63.9 64.7 64.7 64.7 65.1 65.1 65.1 65.3 65.3 65.3 65.3 67.4 67.4 67.4 67.4 68.7 68.7 68.7 68.7 69.0 70.4 70.4 71.2 71.2 71.2 73.0 73.0 73.1 73.1 74.6 74.6 74.6 74.6 79.3 79.3 79.3 79.3 83.0 83.0 83.0 (a) Create a frequency distribution table. The table should have the following columns: class, frequency and relative frequency. (b) Draw the Histogram of frequencies. (c) Calculate the mean and standard deviation of the sample using the formulas of grouped data. Expand the above table, add more columns needed for the calculations. Show all calculations, Do not skip any step. Problem 2. (a) Write the sample space for the following experiments: () A coin is tossed three times. (11) A coin is tossed first and then a dice is rolled. (b ) For the experiment in which the number of pumps in use at a single six-pump gas station is observed. let A = {0. 1, 2. 3. 4). B = {3, 4. 5. 6). and C = {1. 3. 5}. write the set of outcomes of the following events: A' AUB BUC (AnB) UC (An C) UB (An C)