Blade Weight Analysis The dataset Blade Weight shows 350 measurements of blade w

Question

Blade Weight Analysis The dataset Blade Weight shows 350 measurements of blade weights (in pounds) taken from a manufacturing process that produces mower blades during the most recent shift. You are asked to study this data from an analytics perspective. Drawing upon your experience, you have developed a number of questions: 1. What is the mean and standard deviation of the blade weights? 2. Assuming that the data are normal, what is the probability that the blade weights from this process will be less than 4.80 pounds? 3. What is the probability that the blade weights from this process will be greater than 5.20 pounds? 4. What is the probability that the blade weights from this process will be between 4.80 and 5.20 pounds? 5. What is the blade weight exceeded by at most 15% of the blades? (Inverse) (cumulative) 6. Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of blade weights? 7. Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process of materials? (z-score??) (weights will be your y axis???) Write a formal report summarizing your results for each question.

Blade Weight Sample Weight 1 4.88 2 4.92 3 5.02 4 4.97 5 5.00 6 4.99 7 4.86 8 5.07 9 5.04 10 4.87 11 4.77 12 5.14 13 5.04 14 5.00 15 4.88 16 4.91 17 5.09 18 4.97 19 4.98 20 5.07 21 5.03 22 5.12 23 5.08 24 4.86 25 5.11 26 4.92 27 5.18 28 4.93 29 5.12 30 5.08 31 4.75 32 4.99 33 5.00 34 4.91 35 5.18 36 4.95 37 4.63 38 4.89 39 5.11 40 5.05 41 5.03 42 5.02 43 4.96 44 5.04 45 4.93 46 5.06 47 5.07 48 5.00 49 5.03 50 5.00 51 4.95 52 4.99 53 5.02 54 4.90 55 5.10 56 5.01 57 4.84 58 5.01 59 4.88 60 4.97 61 4.97 62 5.06 63 5.06 64 5.04 65 4.87 66 5.00 67 5.03 68 5.02 69 5.02 70 5.06 71 5.21 72 5.09 73 4.97 74 5.01 75 4.90 76 4.89 77 4.93 78 5.16 79 5.02 80 5.01 81 5.10 82 5.03 83 5.07 84 4.92 85 5.08 86 4.96 87 4.74 88 4.91 89 5.12 90 5.00 91 4.93 92 4.88 93 4.88 94 4.81 95 5.16 96 5.03 97 4.87 98 5.09 99 4.94 100 5.08 101 4.97 102 5.23 103 5.12 104 5.09 105 5.12 106 4.93 107 4.79 108 5.10 109 5.12 110 4.86 111 5.00 112 4.94 113 4.95 114 4.95 115 4.87 116 5.09 117 4.94 118 5.01 119 5.04 120 5.05 121 5.05 122 4.97 123 4.96 124 4.96 125 4.99 126 5.04 127 4.91 128 5.19 129 5.03 130 4.99 131 5.12 132 4.97 133 4.88 134 5.07 135 5.01 136 4.89 137 4.95 138 5.09 139 5.09 140 4.89 141 4.93 142 4.85 143 5.03 144 4.92 145 5.09 146 4.99 147 4.92 148 4.87 149 4.90 150 5.02 151 5.21 152 5.02 153 4.9 154 5 155 5.16 156 5.03 157 4.96 158 5.04 159 4.98 160 5.07 161 5.02 162 5.08 163 4.85 164 4.9 165 4.97 166 5.09 167 4.89 168 4.87 169 5.01 170 4.97 171 5.87 172 5.33 173 5.11 174 5.07 175 4.93 176 4.99 177 5.04 178 5.14 179 5.09 180 5.06 181 4.85 182 4.93 183 5.04 184 5.09 185 5.07 186 4.99 187 5.01 188 4.88 189 4.93 190 5.1 191 4.94 192 4.88 193 4.89 194 4.89 195 4.85 196 4.82 197 5.02 198 4.9 199 4.73 200 5.04 201 5.07 202 4.81 203 5.04 204 5.03 205 5.01 206 5.14 207 5.12 208 4.89 209 4.91 210 4.97 211 4.98 212 5.01 213 5.01 214 5.09 215 4.93 216 5.04 217 5.11 218 5.07 219 4.95 220 4.86 221 5.13 222 4.95 223 5.22 224 4.81 225 4.91 226 4.95 227 4.94 228 4.81 229 5.11 230 4.81 231 4.97 232 5.07 233 5.03 234 4.81 235 4.95 236 4.89 237 5.08 238 4.93 239 4.99 240 4.94 241 5.13 242 5.02 243 5.07 244 4.82 245 5.03 246 4.85 247 4.89 248 4.82 249 5.18 250 5.02 251 5.05 252 4.88 253 5.08 254 4.98 255 5.02 256 4.99 257 5.02 258 5.03 259 5.02 260 5.07 261 4.95 262 4.95 263 4.94 264 5.12 265 5.08 266 4.91 267 4.96 268 4.96 269 4.94 270 5.19 271 4.91 272 5.01 273 4.93 274 5.05 275 4.96 276 4.92 277 4.95 278 5.08 279 4.97 280 5.04 281 4.94 282 4.98 283 5.03 284 5.05 285 4.91 286 5.09 287 5.21 288 4.87 289 5.02 290 4.81 291 4.96 292 5.06 293 4.86 294 4.96 295 4.99 296 4.94 297 5.06 298 4.95 299 5.02 300 5.01 301 5.04 302 5.01 303 5.02 304 5.03 305 5.18 306 5.08 307 5.14 308 4.92 309 4.97 310 4.92 311 5.14 312 4.92 313 5.03 314 4.98 315 4.76 316 4.94 317 4.92 318 4.91 319 4.96 320 5.02 321 5.13 322 5.13 323 4.92 324 4.98 325 4.89 326 4.88 327 5.11 328 5.11 329 5.08 330 5.03 331 4.94 332 4.88 333 4.91 334 4.86 335 4.89 336 4.91 337 4.87 338 4.93 339 5.14 340 4.87 341 4.98 342 4.88 343 4.88 344 5.01 345 4.93 346 4.93 347 4.99 348 4.91 349 4.96 350 4.78

Explanation / Answer

1. What is the mean and standard deviation of the blade weights?

Solution:

From the given data, we have

Mean = Xbar = 4.9908

Standard deviation = 0.109288

(By using Excel)

2. Assuming that the data are normal, what is the probability that the blade weights from this process will be less than 4.80 pounds?

Solution:

We have to find P(X<4.80)

Z = (X – mean) / SD

Z = (4.80 – 4.9908) / 0.109288

Z = -1.7458

P(X<4.80) = P(Z<-1.7458) = 0.040419

Required probability = 0.040419

3. What is the probability that the blade weights from this process will be greater than 5.20 pounds?

Solution:

We have to find P(X>5.20)

P(X>5.20) = 1 – P(X<5.20)

Z = (X – mean) / SD

Z = (5.20 - 4.9908) / 0.109288

Z = 1.91421

P(X<5.20) = P(Z<1.91421) = 0.972203

P(X>5.20) = 1 – P(X<5.20)

P(X>5.20) = 1 – 0.972203

P(X>5.20) = 0.027797

Required probability = 0.027797

4. What is the probability that the blade weights from this process will be between 4.80 and 5.20 pounds?

Solution:

We have to find P(4.80<X<5.20)

P(4.80<X<5.20) = P(X<5.20) – P(X<4.80)

Z score for X = 4.80

Z = (X – mean) / SD

Z = (4.80 – 4.9908) / 0.109288

Z = -1.7458

P(X<4.80) = P(Z<-1.7458) = 0.040419

Z score for X = 5.20

Z = (X – mean) / SD

Z = (5.20 - 4.9908) / 0.109288

Z = 1.91421

P(X<5.20) = P(Z<1.91421) = 0.972203

P(4.80<X<5.20) = P(X<5.20) – P(X<4.80) = 0.972203 - 0.040419 = 0.931784

Required probability = 0.931784

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