Reaction time is normally distributed, with a mean of 0.7 sec and a standard deviation of 0.1 sec. Find the probability that an individual selected at random has the following reaction times. (Round your answers to four decimal places.)(a) greater than 0.9 sec(b) less than 0.6 sec(c) between 0.6 and 0.9 sec Areas Under the StandardNormal Curve0 Z0The value of A is the area under the standard normal curve between z = 0 and z = z, for z, 2 0. Areas for negative valuesof z, are obtained by symmetry.z.АZ,AZ.AZ.A0.000.00000.430.16640.860.30511.290.40150.010.00400.440.17000.870.30781.300.40320.020.030.040.880.890.00800.450.17360.31061.310.40490.17720.18080.01200.460.31331.320.40660.01600.470.900.31591.330.40820.050.01990.480.18440.910.31861.340.40990.060.02390.490.18790.920.32121.350.41150.070.02790.500.19150.930.32381.360.41310.080.03190.510.19500.940.32641.370.41470.090.03590.520.19850.950.32891.380.41620.03980.04380.100.530.20190.960.33151.390.41770.110.540.20540.970.33401.400.41920.980.33650.42070.42220.120.04780.550.20881.410.130.05170.560.21230.990.33891.420.140.05570.570.21571.000.34131.430.42360.150.05960.580.21901.010.34381.440.42510.06360.06750.160.590.22241.020.34611.450.42651.461.471.481.490.170.600.22571.030.34850.42790.610.620.630.180.07140.22911.040.35080.42920.190.07540.23241.050.35310.43060.200.07930.23571.060.35540.43191.071.080.210.08320.640.23890.35771.500.43320.220.08710.650.24220.35991.510.43450.36211.521.530.230.09100.660.24541.090.43570.240.09480.670.24861.100.36430.43700.250.09870.680.25171.110.36651.540.43820.260.10260.690.25491.120.36861.550.43940.37081.561.570.270.10640.700.25801.130.44060.280.11030.710.26111.140.37290.44180.290.11410.720.26421.150.37491.580.44290.11790.12170.12550.12930.26731.590.44410.44520.44630.300.731.160.37700.37901.601.610.310.740.27041.170.320.750.27341.180.38100.330.760.27641.190.38301.620.44740.44840.44950.45050.45150.45250.45350.45450.340.13310.770.27941.200.38491.630.350.13680.780.28231.210.38691.640.360.14060.790.28521.220.38881.650.370.14430.800.28811.230.39071.660.380.14800.810.29101.240.39251.670.390.15170.820.29391.250.39441.680.400.15540.830.29671.260.39621.690.410.15910.840.29951.270.39801.700.45540.420.16280.850.30231.280.39971.710.4564АР-44

Mean = 0.7 Standard deviation = 0.1

Answered: Reaction time is normally distributed,…

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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Question

Reaction time is normally distributed, with a mean of 0.7 sec and a standard deviation of 0.1 sec. Find the probability that an individual selected at random has the following reaction times. (Round your answers to four decimal places.)

(a) greater than 0.9 sec

(b) less than 0.6 sec

(c) between 0.6 and 0.9 sec

Areas Under the Standard
Normal Curve
0 Z0
The value of A is the area under the standard normal curve between z = 0 and z = z, for z, 2 0. Areas for negative values
of z, are obtained by symmetry.
z.
А
Z,
A
Z.
A
Z.
A
0.00
0.0000
0.43
0.1664
0.86
0.3051
1.29
0.4015
0.01
0.0040
0.44
0.1700
0.87
0.3078
1.30
0.4032
0.02
0.03
0.04
0.88
0.89
0.0080
0.45
0.1736
0.3106
1.31
0.4049
0.1772
0.1808
0.0120
0.46
0.3133
1.32
0.4066
0.0160
0.47
0.90
0.3159
1.33
0.4082
0.05
0.0199
0.48
0.1844
0.91
0.3186
1.34
0.4099
0.06
0.0239
0.49
0.1879
0.92
0.3212
1.35
0.4115
0.07
0.0279
0.50
0.1915
0.93
0.3238
1.36
0.4131
0.08
0.0319
0.51
0.1950
0.94
0.3264
1.37
0.4147
0.09
0.0359
0.52
0.1985
0.95
0.3289
1.38
0.4162
0.0398
0.0438
0.10
0.53
0.2019
0.96
0.3315
1.39
0.4177
0.11
0.54
0.2054
0.97
0.3340
1.40
0.4192
0.98
0.3365
0.4207
0.4222
0.12
0.0478
0.55
0.2088
1.41
0.13
0.0517
0.56
0.2123
0.99
0.3389
1.42
0.14
0.0557
0.57
0.2157
1.00
0.3413
1.43
0.4236
0.15
0.0596
0.58
0.2190
1.01
0.3438
1.44
0.4251
0.0636
0.0675
0.16
0.59
0.2224
1.02
0.3461
1.45
0.4265
1.46
1.47
1.48
1.49
0.17
0.60
0.2257
1.03
0.3485
0.4279
0.61
0.62
0.63
0.18
0.0714
0.2291
1.04
0.3508
0.4292
0.19
0.0754
0.2324
1.05
0.3531
0.4306
0.20
0.0793
0.2357
1.06
0.3554
0.4319
1.07
1.08
0.21
0.0832
0.64
0.2389
0.3577
1.50
0.4332
0.22
0.0871
0.65
0.2422
0.3599
1.51
0.4345
0.3621
1.52
1.53
0.23
0.0910
0.66
0.2454
1.09
0.4357
0.24
0.0948
0.67
0.2486
1.10
0.3643
0.4370
0.25
0.0987
0.68
0.2517
1.11
0.3665
1.54
0.4382
0.26
0.1026
0.69
0.2549
1.12
0.3686
1.55
0.4394
0.3708
1.56
1.57
0.27
0.1064
0.70
0.2580
1.13
0.4406
0.28
0.1103
0.71
0.2611
1.14
0.3729
0.4418
0.29
0.1141
0.72
0.2642
1.15
0.3749
1.58
0.4429
0.1179
0.1217
0.1255
0.1293
0.2673
1.59
0.4441
0.4452
0.4463
0.30
0.73
1.16
0.3770
0.3790
1.60
1.61
0.31
0.74
0.2704
1.17
0.32
0.75
0.2734
1.18
0.3810
0.33
0.76
0.2764
1.19
0.3830
1.62
0.4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4535
0.4545
0.34
0.1331
0.77
0.2794
1.20
0.3849
1.63
0.35
0.1368
0.78
0.2823
1.21
0.3869
1.64
0.36
0.1406
0.79
0.2852
1.22
0.3888
1.65
0.37
0.1443
0.80
0.2881
1.23
0.3907
1.66
0.38
0.1480
0.81
0.2910
1.24
0.3925
1.67
0.39
0.1517
0.82
0.2939
1.25
0.3944
1.68
0.40
0.1554
0.83
0.2967
1.26
0.3962
1.69
0.41
0.1591
0.84
0.2995
1.27
0.3980
1.70
0.4554
0.42
0.1628
0.85
0.3023
1.28
0.3997
1.71
0.4564
АР-44

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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