Use the table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table. A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 54.1 mm and a standard deviation of 2.9 mm. What percent of the butterflies had the following wingspans? (Round your answers to one decimal place.) (a) less than 48.8 mm  % (b) between 50 and 56 mm

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Use the table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.

A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 54.1 mm and a standard deviation of 2.9 mm. What percent of the butterflies had the following wingspans? (Round your answers to one decimal place.)

(a) less than 48.8 mm
 %

(b) between 50 and 56 mm
 %
Area Under the Standard Normal Curve
A
A
A
A
A
0.00
0.000
0.56
0.212
1.12
0.369
1.68
0.454
2.24
0.487
2.80
0.497
0.01
0.004
0.57
0.216
1.13
0.371
1.69
0.454
2.25
0.488
2.81
0.498
0.02
0.008
0.58
0.219
1.14
0.373
1.70
0.455
2.26
0.488
2.82
0.498
0.03
0.012
0.59
0.222
1.15
0.375
1.71
0.456
2.27
0.488
2.83
0.498
0.04
0.016
0.60
0.226
1.16
0.377
1.72
0.457
2.28
0.489
2.84
0.498
0.458
0.459
0.05
0.020
0.61
0.229
1.17
0.379
1.73
2.29
0.489
2.85
0.498
0.06
0.024
0.62
0.232
1.18
0.381
1.74
2.30
0.489
2.86
0.498
0.07
0.028
0.63
0.236
1.19
0.383
1.75
0.460
2.31
0.490
2.87
0.498
0.08
0.032
0.64
0.239
1.20
0.385
1.76
0.461
2.32
0.490
2.88
0.498
0.09
0.036
0.65
0.242
1.21
0.387
1.77
0.462
2.33
0.490
2.89
0.498
0.10
0.040
0.66
0.245
1.22
0.389
1.78
0.462
2.34
0.490
2.90
0.498
0.391
0.393
0.11
0.044
0.67
0.249
1.23
1.79
0.463
2.35
0.491
2.91
0.498
0.12
0.048
0.68
0.252
1.24
1.80
0.464
2.36
0.491
2.92
0.498
0.13
0.052
0.69
0.255
1.25
0.394
1.81
0.465
2.37
0.491
2.93
0.498
0.14
0.056
0.70
0.258
1.26
0.396
1.82
0.466
2.38
0.491
2.94
0.498
1.27
2.95
0.261
0.264
0.15
0.060
0.71
0.398
1.83
0.466
2.39
0.492
0.498
0.16
0.064
0.72
1.28
0.400
1.84
0.467
2.40
0.492
2.96
0.498
0.17
0.067
0.73
0.267
1.29
0.401
1.85
0.468
2.41
0.492
2.97
0.499
0.18
0.071
0.74
0.270
1.30
0.403
1.86
0.469
2.42
0.492
2.98
0.499
0.19
0.075
0.75
0.273
1.31
0.405
1.87
0.469
2.43
0.492
2.99
0.499
0.20
0.079
0.76
0.276
1.32
0.407
1.88
0.470
2.44
0.493
3.00
0.499
0.21
0.083
0.77
0.279
1.33
0.408
1.89
0.471
2.45
0.493
3.01
0.499
0.22
0.087
0.78
0.282
1.34
0.410
1.90
0.471
2.46
0.493
3.02
0.499
0.23
0.091
0.79
0.285
1.35
0.411
1.91
0.472
2.47
0.493
3.03
0.499
0.24
0.095
0.80
0.288
1.36
0.413
1.92
0.473
2.48
0.493
3.04
0.499
0.25
0.099
0.81
0.291
1.37
0.415
1.93
0.473
2.49
0.494
3.05
0.499
0.26
0.103
0.82
0.294
1.38
0.416
1.94
0.474
2.50
0.494
3.06
0.499
0.27
0.106
0.83
0.297
1.39
0.418
1.95
0.474
2.51
0.494
3.07
0.499
0.499
0.499
0.28
0.110
0.84
0.300
1.40
0.419
1.96
0.475
2.52
0.494
3.08
0.29
0.114
0.85
0.302
1.41
0.421
1.97
0.476
2.53
0.494
3.09
0.118
0.122
0.30
0.86
0.305
1.42
0.422
1.98
0.476
2.54
0.494
3.10
0.499
0.499
0.499
0.31
0.87
0.308
1.43
0.424
1.99
0.477
2.55
0.495
3.11
0.32
0.126
0.88
0.311
1.44
0.425
2.00
0.477
2.56
0.495
3.12
0.33
0.129
0.89
0.313
1.45
0.426
2.01
0.478
2.57
0.495
3.13
0.499
0.34
0.133
0.90
0.316
1.46
0.428
2.02
0.478
2.58
0.495
3.14
0.499
0.35
0.137
0.91
0.319
1.47
0.429
2.03
0.479
2.59
0.495
3.15
0.499
0.36
0.141
0.92
0.321
1.48
0.431
2.04
0.479
2.60
0.495
3.16
0.499
0.37
0.144
0.93
0.324
1.49
0.432
2.05
0.480
2.61
0.495
3.17
0.499
0.38
0.148
0.94
0.326
1.50
0.433
2.06
0.480
2.62
0.496
3.18
0.499
0.39
0.152
0.95
0.329
1.51
0.434
2.07
0.481
2.63
0.496
3.19
0.499
0.40
0.155
0.96
0.331
1.52
0.436
2.08
0.481
2.64
0.496
3.20
0.499
0.499
0.499
0.41
0.159
0.97
0.334
1.53
0.437
2.09
0.482
2.65
0.496
3.21
0.42
0.163
0.98
0.336
1.54
0.438
2.10
0.482
2.66
0.496
3.22
0.43
0.166
0.99
0.339
1.55
0.439
2.11
0.483
2.67
0.496
3.23
0.499
0.44
0.170
1.00
0.341
1.56
0.441
2.12
0.483
2.68
0.496
3.24
0.499
0.45
0.174
1.01
0.344
1.57
0.442
2.13
0.483
2.69
0.496
3.25
0.499
0.46
0.177
1.02
0.346
1.58
0.443
2.14
0.484
2.70
0.497
3.26
0.499
0.47
0.181
1.03
0.348
1.59
0.444
2.15
0.484
2.71
0.497
3.27
0.499
0.48
0.184
1.04
0.351
1.60
0.445
2.16
0.485
2.72
0.497
3.28
0.499
0.49
0.188
1.05
0.353
1.61
0.446
2.17
0.485
2.73
0.497
3.29
0.499
0.50
0.191
1.06
0.355
1.62
0.447
2.18
0.485
2.74
0.497
3.30
0.500
0.51
0.195
1.07
0.358
1.63
0.448
2.19
0.486
2.75
0.497
3.31
0.500
0.52
0.198
1.08
0.360
1.64
0.449
2.20
0.486
2.76
0.497
3.32
0.500
0.53
0.202
1.09
0.362
1.65
0.451
2.21
0.486
2.77
0.497
3.33
0.500
0.54
0.205
1.10
0.364
1.66
0.452
2.22
0.487
2.78
0.497
0.55
0.209
1.11
0.367
1.67
0.453
2.23
0.487
2.79
0.497
Transcribed Image Text:Area Under the Standard Normal Curve A A A A A 0.00 0.000 0.56 0.212 1.12 0.369 1.68 0.454 2.24 0.487 2.80 0.497 0.01 0.004 0.57 0.216 1.13 0.371 1.69 0.454 2.25 0.488 2.81 0.498 0.02 0.008 0.58 0.219 1.14 0.373 1.70 0.455 2.26 0.488 2.82 0.498 0.03 0.012 0.59 0.222 1.15 0.375 1.71 0.456 2.27 0.488 2.83 0.498 0.04 0.016 0.60 0.226 1.16 0.377 1.72 0.457 2.28 0.489 2.84 0.498 0.458 0.459 0.05 0.020 0.61 0.229 1.17 0.379 1.73 2.29 0.489 2.85 0.498 0.06 0.024 0.62 0.232 1.18 0.381 1.74 2.30 0.489 2.86 0.498 0.07 0.028 0.63 0.236 1.19 0.383 1.75 0.460 2.31 0.490 2.87 0.498 0.08 0.032 0.64 0.239 1.20 0.385 1.76 0.461 2.32 0.490 2.88 0.498 0.09 0.036 0.65 0.242 1.21 0.387 1.77 0.462 2.33 0.490 2.89 0.498 0.10 0.040 0.66 0.245 1.22 0.389 1.78 0.462 2.34 0.490 2.90 0.498 0.391 0.393 0.11 0.044 0.67 0.249 1.23 1.79 0.463 2.35 0.491 2.91 0.498 0.12 0.048 0.68 0.252 1.24 1.80 0.464 2.36 0.491 2.92 0.498 0.13 0.052 0.69 0.255 1.25 0.394 1.81 0.465 2.37 0.491 2.93 0.498 0.14 0.056 0.70 0.258 1.26 0.396 1.82 0.466 2.38 0.491 2.94 0.498 1.27 2.95 0.261 0.264 0.15 0.060 0.71 0.398 1.83 0.466 2.39 0.492 0.498 0.16 0.064 0.72 1.28 0.400 1.84 0.467 2.40 0.492 2.96 0.498 0.17 0.067 0.73 0.267 1.29 0.401 1.85 0.468 2.41 0.492 2.97 0.499 0.18 0.071 0.74 0.270 1.30 0.403 1.86 0.469 2.42 0.492 2.98 0.499 0.19 0.075 0.75 0.273 1.31 0.405 1.87 0.469 2.43 0.492 2.99 0.499 0.20 0.079 0.76 0.276 1.32 0.407 1.88 0.470 2.44 0.493 3.00 0.499 0.21 0.083 0.77 0.279 1.33 0.408 1.89 0.471 2.45 0.493 3.01 0.499 0.22 0.087 0.78 0.282 1.34 0.410 1.90 0.471 2.46 0.493 3.02 0.499 0.23 0.091 0.79 0.285 1.35 0.411 1.91 0.472 2.47 0.493 3.03 0.499 0.24 0.095 0.80 0.288 1.36 0.413 1.92 0.473 2.48 0.493 3.04 0.499 0.25 0.099 0.81 0.291 1.37 0.415 1.93 0.473 2.49 0.494 3.05 0.499 0.26 0.103 0.82 0.294 1.38 0.416 1.94 0.474 2.50 0.494 3.06 0.499 0.27 0.106 0.83 0.297 1.39 0.418 1.95 0.474 2.51 0.494 3.07 0.499 0.499 0.499 0.28 0.110 0.84 0.300 1.40 0.419 1.96 0.475 2.52 0.494 3.08 0.29 0.114 0.85 0.302 1.41 0.421 1.97 0.476 2.53 0.494 3.09 0.118 0.122 0.30 0.86 0.305 1.42 0.422 1.98 0.476 2.54 0.494 3.10 0.499 0.499 0.499 0.31 0.87 0.308 1.43 0.424 1.99 0.477 2.55 0.495 3.11 0.32 0.126 0.88 0.311 1.44 0.425 2.00 0.477 2.56 0.495 3.12 0.33 0.129 0.89 0.313 1.45 0.426 2.01 0.478 2.57 0.495 3.13 0.499 0.34 0.133 0.90 0.316 1.46 0.428 2.02 0.478 2.58 0.495 3.14 0.499 0.35 0.137 0.91 0.319 1.47 0.429 2.03 0.479 2.59 0.495 3.15 0.499 0.36 0.141 0.92 0.321 1.48 0.431 2.04 0.479 2.60 0.495 3.16 0.499 0.37 0.144 0.93 0.324 1.49 0.432 2.05 0.480 2.61 0.495 3.17 0.499 0.38 0.148 0.94 0.326 1.50 0.433 2.06 0.480 2.62 0.496 3.18 0.499 0.39 0.152 0.95 0.329 1.51 0.434 2.07 0.481 2.63 0.496 3.19 0.499 0.40 0.155 0.96 0.331 1.52 0.436 2.08 0.481 2.64 0.496 3.20 0.499 0.499 0.499 0.41 0.159 0.97 0.334 1.53 0.437 2.09 0.482 2.65 0.496 3.21 0.42 0.163 0.98 0.336 1.54 0.438 2.10 0.482 2.66 0.496 3.22 0.43 0.166 0.99 0.339 1.55 0.439 2.11 0.483 2.67 0.496 3.23 0.499 0.44 0.170 1.00 0.341 1.56 0.441 2.12 0.483 2.68 0.496 3.24 0.499 0.45 0.174 1.01 0.344 1.57 0.442 2.13 0.483 2.69 0.496 3.25 0.499 0.46 0.177 1.02 0.346 1.58 0.443 2.14 0.484 2.70 0.497 3.26 0.499 0.47 0.181 1.03 0.348 1.59 0.444 2.15 0.484 2.71 0.497 3.27 0.499 0.48 0.184 1.04 0.351 1.60 0.445 2.16 0.485 2.72 0.497 3.28 0.499 0.49 0.188 1.05 0.353 1.61 0.446 2.17 0.485 2.73 0.497 3.29 0.499 0.50 0.191 1.06 0.355 1.62 0.447 2.18 0.485 2.74 0.497 3.30 0.500 0.51 0.195 1.07 0.358 1.63 0.448 2.19 0.486 2.75 0.497 3.31 0.500 0.52 0.198 1.08 0.360 1.64 0.449 2.20 0.486 2.76 0.497 3.32 0.500 0.53 0.202 1.09 0.362 1.65 0.451 2.21 0.486 2.77 0.497 3.33 0.500 0.54 0.205 1.10 0.364 1.66 0.452 2.22 0.487 2.78 0.497 0.55 0.209 1.11 0.367 1.67 0.453 2.23 0.487 2.79 0.497
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