00 .000 56 212 1.12 369 1.68 454 224 488 280 497 01 004 57 216 1.13 371 1.69 455 225 48S 281 498 455 226 227 228 AS8 2.82 498 58 59 223 60 226 219 1.14 373 02 008 03 012 04 016 05 1.70 171 .72 1.15 498 498 2 85 375 456 488 283 16 457 489 2.84 377 379 381 229 117 173 458 229 489 498 .020 06 024 61 174 459 230 286 498 489 490 .62 232 LIS 236 1.19 383 L75 460 231 287 498 07 028 OS 032 036 63 239 1.20 385 1.76 461 232 490 2.88 493 .64 242 66 177 1.78 233 289 2.90 387 490 490 09 65 121 462 498 245 67 10 040 1.22 389 463 234 498 463 491 249 68 69 11 044 1.23 391 1.79 235 291 498 236 2.92 393 1.25 491 498 .048 052 12 252 124 130 454 465 255 258 237 491 .498 2.93 294 195 13 394 1.82 466 238 498 70 71 .056 1.26 396 491 14 060 064 261 72 15 127 398 1.83 466 2.39 492 498 16 264 128 400 184 467 2.40 492 2.96 499 17 068 73 267 1.29 402 1.85 468 241 493 297 499 1 86 492 499 298 2.99 18 .071 .74 270 1.30 403 469 242 19 075 .75 273 131 405 187 469 243 493 499 3.00 3.01 3.02 3.03 20 079 .76 276 132 493 499 407 408 1.88 470 244 77 279 245 21 083 22 087 13 091 133 1.89 471 493 499 .78 282 79 285 288 .499 400 134 410 190 471 2.46 493 1.35 412 191 472 247 493 499 34 095 80 136 413 191 473 2.48 493 3.04 499 099 473 494 3.05 499 291 82 297 84 25 81 137 415 193 249 474 3.06 499 103 7 106 28 110 29 114 26 416 418 419 1.41 294 135 494 194 195 1.96 250 251 252 2.53 139 474 494 3.07 499 3.08 27 83 300 140 475 476 494 499 85 302 421 197 494 3.09 499 476 254 2.55 2.56 305 1.42 422 1.98 495 3.10 3.11 3.12 3.13 30 118 86 499 31 122 143 199 477 495 499 308 88 89 87 424 477 495 495 495 495 1.44 425 427 428 32 126 311 200 499 145 478 499 499 409 33 201 102 203 2.57 258 129 313 34 133 90 316 1.46 478 3.14 1.47 429 431 137 91 319 479 259 315 499 499 35 36 141 92 321 1.48 204 479 2.60 495 3.16 37 144 93 334 1.49 432 205 480 2.61 496 3.17 499 38 2.06 107 94 1.50 3.18 326 329 148 433 480 262 496 499 39 1.51 435 481 163 496 2.64 153 95 3.19 499 40 155 96 333 1.52 436 2.08 481 496 3 20 499 41 159 97 334 1.53 437 2.09 482 2.65 496 3.21 499 1.54 1.55 42 163 98 337 438 210 482 .496 267 496 2.68 496 2.69 496 2.70 2.66 3.22 323 3.24 499 483 212 213 43 166 99 339 439 211 499 44 170 341 344 1.02 100 1.56 1.57 441 483 499 45 174 1.01 443 483 325 .499 46 177 346 1.58 443 214 484 497 3.26 499 215 216 2.17 2.18 219 2.20 47 181 103 349 1.59 444 434 2.71 497 3.27 500 48 14 1 04 1.60 2.73 500 500 500 300 351 445 497 497 485 3.28 49 188 353 1.06 355 446 447 449 1.05 1.61 485 2.73 3.29 192 195 52 50 162 2.74 497 485 486 330 51 1.07 358 1.63 2.75 497 331 199 202 54 205 55 209 276 1.08 1.09 1.64 450 1.65 451 1.66 452 1.67 453 360 486 497 332 500 53 362 277 500 221 222 223 487 497 333 2.79 497 2.79 497 110 364 487 111 367 487
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Use a table to find a z-score that fits the given conditions. Interpolate if necessary 33% of the area under the standard normal curve is above the score.
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