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 CurveAAAAA0.000.0000.560.2121.120.3691.680.4542.240.4872.800.4970.010.0040.570.2161.130.3711.690.4542.250.4882.810.4980.020.0080.580.2191.140.3731.700.4552.260.4882.820.4980.030.0120.590.2221.150.3751.710.4562.270.4882.830.4980.040.0160.600.2261.160.3771.720.4572.280.4892.840.4980.4580.4590.050.0200.610.2291.170.3791.732.290.4892.850.4980.060.0240.620.2321.180.3811.742.300.4892.860.4980.070.0280.630.2361.190.3831.750.4602.310.4902.870.4980.080.0320.640.2391.200.3851.760.4612.320.4902.880.4980.090.0360.650.2421.210.3871.770.4622.330.4902.890.4980.100.0400.660.2451.220.3891.780.4622.340.4902.900.4980.3910.3930.110.0440.670.2491.231.790.4632.350.4912.910.4980.120.0480.680.2521.241.800.4642.360.4912.920.4980.130.0520.690.2551.250.3941.810.4652.370.4912.930.4980.140.0560.700.2581.260.3961.820.4662.380.4912.940.4981.272.950.2610.2640.150.0600.710.3981.830.4662.390.4920.4980.160.0640.721.280.4001.840.4672.400.4922.960.4980.170.0670.730.2671.290.4011.850.4682.410.4922.970.4990.180.0710.740.2701.300.4031.860.4692.420.4922.980.4990.190.0750.750.2731.310.4051.870.4692.430.4922.990.4990.200.0790.760.2761.320.4071.880.4702.440.4933.000.4990.210.0830.770.2791.330.4081.890.4712.450.4933.010.4990.220.0870.780.2821.340.4101.900.4712.460.4933.020.4990.230.0910.790.2851.350.4111.910.4722.470.4933.030.4990.240.0950.800.2881.360.4131.920.4732.480.4933.040.4990.250.0990.810.2911.370.4151.930.4732.490.4943.050.4990.260.1030.820.2941.380.4161.940.4742.500.4943.060.4990.270.1060.830.2971.390.4181.950.4742.510.4943.070.4990.4990.4990.280.1100.840.3001.400.4191.960.4752.520.4943.080.290.1140.850.3021.410.4211.970.4762.530.4943.090.1180.1220.300.860.3051.420.4221.980.4762.540.4943.100.4990.4990.4990.310.870.3081.430.4241.990.4772.550.4953.110.320.1260.880.3111.440.4252.000.4772.560.4953.120.330.1290.890.3131.450.4262.010.4782.570.4953.130.4990.340.1330.900.3161.460.4282.020.4782.580.4953.140.4990.350.1370.910.3191.470.4292.030.4792.590.4953.150.4990.360.1410.920.3211.480.4312.040.4792.600.4953.160.4990.370.1440.930.3241.490.4322.050.4802.610.4953.170.4990.380.1480.940.3261.500.4332.060.4802.620.4963.180.4990.390.1520.950.3291.510.4342.070.4812.630.4963.190.4990.400.1550.960.3311.520.4362.080.4812.640.4963.200.4990.4990.4990.410.1590.970.3341.530.4372.090.4822.650.4963.210.420.1630.980.3361.540.4382.100.4822.660.4963.220.430.1660.990.3391.550.4392.110.4832.670.4963.230.4990.440.1701.000.3411.560.4412.120.4832.680.4963.240.4990.450.1741.010.3441.570.4422.130.4832.690.4963.250.4990.460.1771.020.3461.580.4432.140.4842.700.4973.260.4990.470.1811.030.3481.590.4442.150.4842.710.4973.270.4990.480.1841.040.3511.600.4452.160.4852.720.4973.280.4990.490.1881.050.3531.610.4462.170.4852.730.4973.290.4990.500.1911.060.3551.620.4472.180.4852.740.4973.300.5000.510.1951.070.3581.630.4482.190.4862.750.4973.310.5000.520.1981.080.3601.640.4492.200.4862.760.4973.320.5000.530.2021.090.3621.650.4512.210.4862.770.4973.330.5000.540.2051.100.3641.660.4522.220.4872.780.4970.550.2091.110.3671.670.4532.230.4872.790.497

Name: Use the table to answer the question. Note: Round z-scores to the near
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Description: 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

Answered: Image /qna-images/answer/baab5726-51e3-416d-bd97-29a694e8c342.jpg

Answered: Use the table to answer the question.…

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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