A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 30 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.)(a) less than 28 mpg(b) greater than 36 mpg(c) between 24 and 36 mpg 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

Given information Mean µ = 30 mpg Standard deviation = 4 mg

Answered: A certain model of automobile has its…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 30 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.)

(a) less than 28 mpg

(b) greater than 36 mpg

(c) between 24 and 36 mpg

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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