In tablet manufacturing operations, common problems encountered include fluctuations in tablet weights and inconsistent tablet hardness. These problems are usually due to uneven powder flow into the die due to poor powder flow properties, uneven feeder material into the tablet press, malfunctions of the pressing machines and many more. A. Describe and summarize the sample data of your assigned Lajak tablet, produced in May 2020. Present the observations effectively: in numerical, tabular and graphical forms.

B. The food and drug administration (FDA) authority requires that weights of standard tablets produced by manufacturers should be normally distribute dwith 350mg with standard deviation of 14mg. Comment on whether there is significance evidence that Lajak tablets produced in May 2020 (regardless of shifts) do follow this distribution. [note: for this test, you first need to collect your data by creating a frequency table with suitable range of values/categories]

C. Comment on whether there is any significance difference between tablet weights(mg) from the different shifts. D. Tablets hardness can be represented by its relative density and tensile strength. Studies have indicated that its tensile strength depends on the relative density, regardless of production shifts. Recently, a batch was found to produce cluster of tablets that show low relative density values of 68%,74.3%, and 80.1%. Based on the current data in May 2021, what is the prediction of the tensile strength for such tablets? Comment on the validity of the model that you have used to carry out this prediction.

29 30 31 32 33 34 35 36 37 38 39 40 Relative Tensile Weight Density Strength mg) (%) (Mpa) Shift 1 351.49 87.4 6.9 Night 2 366.53 87.2 7.2 Evening 3 353.42 86.8 7.2 Evening 4 346.68 84.2 6.9 Evening 5 340.57 92.9 73 Evening 361.12 87.7 7.2 Morning 7 324.48 89.4 7.3 Night 8 359.13 85.5 7 Night 9 344.71 90.1 7.2 Morning 10 346.6 86.5 7.1 Night 11 322.17 86.1 6.9 Moring 12 387.76 88.8 7.1 Evening 13 323.21 89.2 7.3 Morning 14 340.66 87.3 7.1 Evening 15 354 26 90.1 7.4 Night 16 341.69 89.1 7.2 Night 17 344.91 85.3 7 Evening 18 360.19 85.7 7 Morning 19 350.58 91.9 7.5 Evening 20 374.01 87.5 7.2 Morning 21 359.79 88.6 7 Evening 22 346.33 87 7.1 Moming 23 353.08 87.5 7.2 Evening 24 352.89 86.7 7 Night 25 351.82 86.2 7 Night 26 352.95 87.9 7.2 Evening 27 331.33 89.1 7.2 Morning 28 349.81 84.4 6.9 Morning 42 43 44 45 48 353 25 378.89 352.75 359.04 346.42 358.22 345.58 346.79 345.46 356.62 337.6 365.83 378.4 364.45 353.8 377.11 351.31 342.85 325.18 355.5 333.09 332.31 376.61 385.22 351.39 353.79 331.51 358.78 321.5 341.15 86 88.9 87.8 88.7 88.1 91.1 87.8 87.6 87.5 88.3 89.5 88.3 90 91.7 88.9 89.9 85.9 87.8 90.8 86.8 89.6 83.2 88.3 88.4 89.5 85.6 88.9 88.8 88.5 91 6.9 7.4 7.2 7.2 7.2 7.5 7.1 7 7.1 7.2 7.2 7 7.3 7.4 7.2 7.3 6.9 7.2 7.3 7 7.3 6.6 7.2 7.1 7.2 7 7.2 7.1 7.2 7.3 Morning Night Evening Moming Morning Evening Morning Morning Night Night Evening Night Night Night Morning Morning Morning Night Evening Morning Night Evening Evening Night Night Evening Evening Night Evening Night 48 49 50 51 52 53 54 55 56 57 58 7.2 7.2 7.3 7.1 7.3 7.1 7.2 7.2 121 7 7.7 7 7.2 6.9 6.8 7.2 7.4 7.2 7 7 7.1 7.1 7.2 129 59 361.17 60 340.05 61 331.49 62 322.91 63 362.44 64 362.83 65 327.91 66 340.12 67 369.92 68 340.04 69 343.54 70 350.36 71 386.68 72 331.37 73 352.58 74 382.38 75 333.32 78 348.01 77 376.67 78 343.84 79 344.62 80 362.15 81 355.93 82 342.96 83 351.54 84 345.83 85 337.78 86 341.57 87 348.51 88 364.50 89 358.2 90 337.03 91 374.52 92 349.74 93 347.28 94 335.43 95 349.51 96 344.47 97 322.00 98 370.26 99 352.19 100 346.14 101 353.95 102 337.48 103 370.63 104 339.4 105 357.03 108 308.44 107 338.3 108 358.74 109 346.97 110 381.33 111 305.27 112 347.83 86.8 89.3 88.9 89.6 89.7 88.5 88.2 88.3 88.9 93.9 84.3 87.9 86.2 88 87.7 90.6 88.8 87.7 87.5 87.2 85.8 88.8 88 89.9 83.5 90 88.9 90.1 87.7 85.4 85.2 90.9 86.8 87.3 90.2 88.5 88.9 89.1 89.4 88.4 92.2 88.5 88.8 88.3 85.5 90.1 87.5 83.8 88.3 87.6 89.4 88.2 85.9 88 139 Night Evening Evening Night Night Morning Night Night Evening Evening Evening Evening Night Evening Morning Morning Night Night Evening Evening Evening Moming Night Evening Evening Evening Night Morning Evening Night Moring Moming Morning Morning Evening Evening Moming Night Evening Evening Morning Morning Morning Night Night Evening Evening Night Night Morning Evening Morning Morning Evening 89.9 88.9 88.1 85.9 89.2 88 90.9 87.8 89 89.7 87.9 89.3 89.7 89.7 87 89 87.3 89.7 85.3 86.3 87.8 88.2 90.8 89.1 91 93.1 89.4 83.4 88.1 90.1 87.3 85.8 86.7 81.8 113 342.46 114 372.6 115 325.05 116 31655 117 365.94 118 357.44 119 384.36 120 327.29 351.63 122 341.05 123 334.85 124 365.4 125 380.72 128 351.74 127 340.77 128 375.69 357.26 130 368.85 131 320.15 132 320.37 133 315.29 134 322.83 135 320.73 138 348.97 137 344.7 138 349.97 350.9 140 371.4 141 344 54 142 338.27 143 334.83 144 354.64 145 337.98 148 346.58 147 385.49 148 368.87 149 326.14 150 348.35 151 354.75 152 364 316.25 154 357.81 155 336.66 156 340.28 157 368.88 158 344.52 159 362.14 160 359.72 346.37 162 347.87 163 343.96 164 351.51 165 355.22 166 327.41 7.1 6.6 7.4 7.2 7.2 7.2 7.1 8.7 7.4 6.9 7.1 7.3 7.2 7.1 7.4 7.1 7.3 7.6 7.2 7.1 7 6.9 7.3 7.3 6.8 7.3 7.1 7.1 6.9 7 7.2 7.4 7.1 7 7.1 7.3 7.3 7.4 7.1 7.3 7.2 6.9 7.4 7.5 7.2 7.1 7.3 7.1 7.1 7.1 6.8 7.3 7.3 7.2 7.2 7.4 7.5 7.1 6.8 7.2 7.3 7 7 6.8 8.6 7.2 7.1 7.4 7.3 6.9 7 6.9 7.5 7.1 7.2 7.1 7.2 7 7.2 6.8 7.6 7.3 7 7 7 Night Night Night Evening Morning Moring Night Night Moming Evening Morning Morning Moring Evening Moming Night Evening Night Moming Night Night Night Evening Morning Evening Morning Morning Morning Night Night Evening Night Evening Evening Evening Morning Morning Night Morning Morning Evening Morning Evening Morning Evening Evening Morning Evening Evening Evening Night Morning Night Night 88.2 153 87.9 90.7 89.7 86.4 87.7 84.8 91 88.2 87.8 87.6 88.4 86.8 87.7 86.3 90.1 88.4 88.2 85.5 88.9 181 6.9 7.4 7.3 7.3 7.5 167 350.05 168 373.13 169 340.01 170 344.14 171 342.42 172 342.52 173 347.83 174 372.57 175 323.01 176 365.42 177 358.83 178 354.34 179 381.23 180 337.32 181 343.81 182 344.5 183 353.3 84.9 91.1 88.5 90.6 92.8 88.7 89.2 88.9 91.4 88.9 89 86.8 89.3 89.8 88.3 88.2 87.8 7.2 7.1 7 7.3 7.4 7.1 7 7.3 7.3 7.1 7.1 7.1 Night Morning Morning Morning Night Morning Night Evening Morning Night Morning Evening Evening Night Night Morning Evening 184 349.22 185 350.58 188 340.29 187 373.17 188 339.25 189 363.54 190 347.11 191 328.7 192 343.84 193 354.97 194 350.04 195 337.67 196 355.78 197 345.03 198 346.9 199 348.64 200365.31 84.2 89.6 89.3 92.2 80 89.4 88.4 91.3 91.5 87.3 87.4 88.3 88.1 90.2 88.5 86.2 88.7 7 7.3 7.2 7.5 7.3 7.3 7.1 7.5 7.8 7 7.1 7 7 7.4 7.2 6.9 7.4 Morning Evening Night Moming Night Night Evening Morning Evening Evening Evening Evening Morning Night Evening Evening Evening WIN 29 30 31 32 33 34 35 36 37 38 39 40 Relative Tensile Weight Density Strength mg) (%) (Mpa) Shift 1 351.49 87.4 6.9 Night 2 366.53 87.2 7.2 Evening 3 353.42 86.8 7.2 Evening 4 346.68 84.2 6.9 Evening 5 340.57 92.9 73 Evening 361.12 87.7 7.2 Morning 7 324.48 89.4 7.3 Night 8 359.13 85.5 7 Night 9 344.71 90.1 7.2 Morning 10 346.6 86.5 7.1 Night 11 322.17 86.1 6.9 Moring 12 387.76 88.8 7.1 Evening 13 323.21 89.2 7.3 Morning 14 340.66 87.3 7.1 Evening 15 354 26 90.1 7.4 Night 16 341.69 89.1 7.2 Night 17 344.91 85.3 7 Evening 18 360.19 85.7 7 Morning 19 350.58 91.9 7.5 Evening 20 374.01 87.5 7.2 Morning 21 359.79 88.6 7 Evening 22 346.33 87 7.1 Moming 23 353.08 87.5 7.2 Evening 24 352.89 86.7 7 Night 25 351.82 86.2 7 Night 26 352.95 87.9 7.2 Evening 27 331.33 89.1 7.2 Morning 28 349.81 84.4 6.9 Morning 42 43 44 45 48 353 25 378.89 352.75 359.04 346.42 358.22 345.58 346.79 345.46 356.62 337.6 365.83 378.4 364.45 353.8 377.11 351.31 342.85 325.18 355.5 333.09 332.31 376.61 385.22 351.39 353.79 331.51 358.78 321.5 341.15 86 88.9 87.8 88.7 88.1 91.1 87.8 87.6 87.5 88.3 89.5 88.3 90 91.7 88.9 89.9 85.9 87.8 90.8 86.8 89.6 83.2 88.3 88.4 89.5 85.6 88.9 88.8 88.5 91 6.9 7.4 7.2 7.2 7.2 7.5 7.1 7 7.1 7.2 7.2 7 7.3 7.4 7.2 7.3 6.9 7.2 7.3 7 7.3 6.6 7.2 7.1 7.2 7 7.2 7.1 7.2 7.3 Morning Night Evening Moming Morning Evening Morning Morning Night Night Evening Night Night Night Morning Morning Morning Night Evening Morning Night Evening Evening Night Night Evening Evening Night Evening Night 48 49 50 51 52 53 54 55 56 57 58 7.2 7.2 7.3 7.1 7.3 7.1 7.2 7.2 121 7 7.7 7 7.2 6.9 6.8 7.2 7.4 7.2 7 7 7.1 7.1 7.2 129 59 361.17 60 340.05 61 331.49 62 322.91 63 362.44 64 362.83 65 327.91 66 340.12 67 369.92 68 340.04 69 343.54 70 350.36 71 386.68 72 331.37 73 352.58 74 382.38 75 333.32 78 348.01 77 376.67 78 343.84 79 344.62 80 362.15 81 355.93 82 342.96 83 351.54 84 345.83 85 337.78 86 341.57 87 348.51 88 364.50 89 358.2 90 337.03 91 374.52 92 349.74 93 347.28 94 335.43 95 349.51 96 344.47 97 322.00 98 370.26 99 352.19 100 346.14 101 353.95 102 337.48 103 370.63 104 339.4 105 357.03 108 308.44 107 338.3 108 358.74 109 346.97 110 381.33 111 305.27 112 347.83 86.8 89.3 88.9 89.6 89.7 88.5 88.2 88.3 88.9 93.9 84.3 87.9 86.2 88 87.7 90.6 88.8 87.7 87.5 87.2 85.8 88.8 88 89.9 83.5 90 88.9 90.1 87.7 85.4 85.2 90.9 86.8 87.3 90.2 88.5 88.9 89.1 89.4 88.4 92.2 88.5 88.8 88.3 85.5 90.1 87.5 83.8 88.3 87.6 89.4 88.2 85.9 88 139 Night Evening Evening Night Night Morning Night Night Evening Evening Evening Evening Night Evening Morning Morning Night Night Evening Evening Evening Moming Night Evening Evening Evening Night Morning Evening Night Moring Moming Morning Morning Evening Evening Moming Night Evening Evening Morning Morning Morning Night Night Evening Evening Night Night Morning Evening Morning Morning Evening 89.9 88.9 88.1 85.9 89.2 88 90.9 87.8 89 89.7 87.9 89.3 89.7 89.7 87 89 87.3 89.7 85.3 86.3 87.8 88.2 90.8 89.1 91 93.1 89.4 83.4 88.1 90.1 87.3 85.8 86.7 81.8 113 342.46 114 372.6 115 325.05 116 31655 117 365.94 118 357.44 119 384.36 120 327.29 351.63 122 341.05 123 334.85 124 365.4 125 380.72 128 351.74 127 340.77 128 375.69 357.26 130 368.85 131 320.15 132 320.37 133 315.29 134 322.83 135 320.73 138 348.97 137 344.7 138 349.97 350.9 140 371.4 141 344 54 142 338.27 143 334.83 144 354.64 145 337.98 148 346.58 147 385.49 148 368.87 149 326.14 150 348.35 151 354.75 152 364 316.25 154 357.81 155 336.66 156 340.28 157 368.88 158 344.52 159 362.14 160 359.72 346.37 162 347.87 163 343.96 164 351.51 165 355.22 166 327.41 7.1 6.6 7.4 7.2 7.2 7.2 7.1 8.7 7.4 6.9 7.1 7.3 7.2 7.1 7.4 7.1 7.3 7.6 7.2 7.1 7 6.9 7.3 7.3 6.8 7.3 7.1 7.1 6.9 7 7.2 7.4 7.1 7 7.1 7.3 7.3 7.4 7.1 7.3 7.2 6.9 7.4 7.5 7.2 7.1 7.3 7.1 7.1 7.1 6.8 7.3 7.3 7.2 7.2 7.4 7.5 7.1 6.8 7.2 7.3 7 7 6.8 8.6 7.2 7.1 7.4 7.3 6.9 7 6.9 7.5 7.1 7.2 7.1 7.2 7 7.2 6.8 7.6 7.3 7 7 7 Night Night Night Evening Morning Moring Night Night Moming Evening Morning Morning Moring Evening Moming Night Evening Night Moming Night Night Night Evening Morning Evening Morning Morning Morning Night Night Evening Night Evening Evening Evening Morning Morning Night Morning Morning Evening Morning Evening Morning Evening Evening Morning Evening Evening Evening Night Morning Night Night 88.2 153 87.9 90.7 89.7 86.4 87.7 84.8 91 88.2 87.8 87.6 88.4 86.8 87.7 86.3 90.1 88.4 88.2 85.5 88.9 181 6.9 7.4 7.3 7.3 7.5 167 350.05 168 373.13 169 340.01 170 344.14 171 342.42 172 342.52 173 347.83 174 372.57 175 323.01 176 365.42 177 358.83 178 354.34 179 381.23 180 337.32 181 343.81 182 344.5 183 353.3 84.9 91.1 88.5 90.6 92.8 88.7 89.2 88.9 91.4 88.9 89 86.8 89.3 89.8 88.3 88.2 87.8 7.2 7.1 7 7.3 7.4 7.1 7 7.3 7.3 7.1 7.1 7.1 Night Morning Morning Morning Night Morning Night Evening Morning Night Morning Evening Evening Night Night Morning Evening 184 349.22 185 350.58 188 340.29 187 373.17 188 339.25 189 363.54 190 347.11 191 328.7 192 343.84 193 354.97 194 350.04 195 337.67 196 355.78 197 345.03 198 346.9 199 348.64 200365.31 84.2 89.6 89.3 92.2 80 89.4 88.4 91.3 91.5 87.3 87.4 88.3 88.1 90.2 88.5 86.2 88.7 7 7.3 7.2 7.5 7.3 7.3 7.1 7.5 7.8 7 7.1 7 7 7.4 7.2 6.9 7.4 Morning Evening Night Moming Night Night Evening Morning Evening Evening Evening Evening Morning Night Evening Evening Evening WIN