probability and statistics
Joss_Smitx01
chap003.pptMcGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 3
Probability and Statistics
A Foundation for Becoming a More Effective and Efficient Problem Solver
3-*
Normal Distribution
- Common probability distribution
- e.g., height, weight, age, sum of two dice rolled 1,000 times, etc.
3-*
Normal Distribution
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0.0
0.1
0.2
0.30000000000000004
0.4
0.5
0.6
0.7
0.7999999999999999
0.8999999999999999
0.9999999999999999
1.0999999999999999
1.2
1.3
1.4000000000000001
1.5000000000000002
1.6000000000000003
1.7000000000000004
1.8000000000000005
1.9000000000000006
2.0000000000000004
2.1000000000000005
2.2000000000000006
2.3000000000000007
2.400000000000001
2.500000000000001
2.600000000000001
2.700000000000001
2.800000000000001
2.9000000000000012
3.0000000000000013
3.1000000000000014
3.2000000000000015
3.3000000000000016
3.4000000000000017
3.5000000000000018
3.600000000000002
3.700000000000002
3.800000000000002
3.900000000000002
4.000000000000002
4.100000000000001
4.200000000000001
4.300000000000001
4.4
4.5
4.6
4.699999999999999
4.799999999999999
4.899999999999999
4.999999999999998
5.099999999999998
5.1999999999999975
5.299999999999997
5.399999999999997
5.4999999999999964
5.599999999999996
5.699999999999996
5.799999999999995
5.899999999999995
5.999999999999995
6.099999999999994
6.199999999999994
6.299999999999994
6.399999999999993
6.499999999999993
6.5999999999999925
6.699999999999992
6.799999999999992
6.8999999999999915
6.999999999999991
7.099999999999991
7.19999999999999
7.29999999999999
7.39999999999999
7.499999999999989
7.599999999999989
7.699999999999989
7.799999999999988
7.899999999999988
7.999999999999988
1.3383022576488534E-4
1.986554713927727E-4
2.919469257914602E-4
4.247802705507514E-4
6.119019301137718E-4
8.726826950457599E-4
0.0012322191684730197
0.001722568939053681
0.00238408820146484
0.0032668190561999178
0.0044318484119380075
0.005952532419775848
0.007915451582979967
0.01042093481442259
0.013582969233685632
0.017528300493568537
0.022394530294842927
0.028327037741601183
0.03547459284623148
0.043983595980427226
0.0539909665131881
0.06561581477467664
0.07895015830089423
0.09404907737688703
0.11092083467945568
0.1295175956658919
0.14972746563574504
0.17136859204780758
0.19418605498321317
0.21785217703255083
0.2419707245191437
0.26608524989875515
0.28969155276148306
0.3122539333667616
0.33322460289179995
0.3520653267642998
0.36827014030332356
0.3813878154605243
0.391042693975456
0.3969525474770118
0.39894228040143265
0.3969525474770117
0.39104269397545577
0.38138781546052397
0.3682701403033232
0.35206532676429947
0.33322460289179967
0.3122539333667614
0.28969155276148295
0.26608524989875515
0.24197072451914378
0.21785217703255105
0.1941860549832135
0.17136859204780797
0.14972746563574552
0.1295175956658924
0.11092083467945624
0.0940490773768876
0.07895015830089482
0.0656158147746772
0.053990966513188625
0.04398359598042771
0.0354745928462319
0.02832703774160159
0.022394530294843257
0.01752830049356885
0.013582969233685878
0.010420934814422817
0.007915451582980144
0.005952532419776001
0.004431848411938125
0.003266819056200014
0.0023840882014649163
0.0017225689390537363
0.0012322191684730624
8.726826950457925E-4
6.119019301137963E-4
4.247802705507695E-4
2.9194692579147323E-4
1.9865547139278204E-4
1.3383022576489198E-4
0.0
1.3383022576488534E-4
0.1
1.986554713927727E-4
0.2
2.919469257914602E-4
0.30000000000000004
4.247802705507514E-4
0.4
6.119019301137718E-4
0.5
8.726826950457599E-4
0.6
0.0012322191684730197
0.7
0.001722568939053681
0.7999999999999999
0.00238408820146484
0.8999999999999999
0.0032668190561999178
0.9999999999999999
0.0044318484119380075
1.0999999999999999
0.005952532419775848
1.2
0.007915451582979967
1.3
0.01042093481442259
1.4000000000000001
0.013582969233685632
1.5000000000000002
0.017528300493568537
1.6000000000000003
0.022394530294842927
1.7000000000000004
0.028327037741601183
1.8000000000000005
0.03547459284623148
1.9000000000000006
0.043983595980427226
2.0000000000000004
0.0539909665131881
2.1000000000000005
0.06561581477467664
2.2000000000000006
0.07895015830089423
2.3000000000000007
0.09404907737688703
2.400000000000001
0.11092083467945568
2.500000000000001
0.1295175956658919
2.600000000000001
0.14972746563574504
2.700000000000001
0.17136859204780758
2.800000000000001
0.19418605498321317
2.9000000000000012
0.21785217703255083
3.0000000000000013
0.2419707245191437
3.1000000000000014
0.26608524989875515
3.2000000000000015
0.28969155276148306
3.3000000000000016
0.3122539333667616
3.4000000000000017
0.33322460289179995
3.5000000000000018
0.3520653267642998
3.600000000000002
0.36827014030332356
3.700000000000002
0.3813878154605243
3.800000000000002
0.391042693975456
3.900000000000002
0.3969525474770118
4.000000000000002
0.39894228040143265
4.100000000000001
0.3969525474770117
4.200000000000001
0.39104269397545577
4.300000000000001
0.38138781546052397
4.4
0.3682701403033232
4.5
0.35206532676429947
4.6
0.33322460289179967
4.699999999999999
0.3122539333667614
4.799999999999999
0.28969155276148295
4.899999999999999
0.26608524989875515
4.999999999999998
0.24197072451914378
5.099999999999998
0.21785217703255105
5.1999999999999975
0.1941860549832135
5.299999999999997
0.17136859204780797
5.399999999999997
0.14972746563574552
5.4999999999999964
0.1295175956658924
5.599999999999996
0.11092083467945624
5.699999999999996
0.0940490773768876
5.799999999999995
0.07895015830089482
5.899999999999995
0.0656158147746772
5.999999999999995
0.053990966513188625
6.099999999999994
0.04398359598042771
6.199999999999994
0.0354745928462319
6.299999999999994
0.02832703774160159
6.399999999999993
0.022394530294843257
6.499999999999993
0.01752830049356885
6.5999999999999925
0.013582969233685878
6.699999999999992
0.010420934814422817
6.799999999999992
0.007915451582980144
6.8999999999999915
0.005952532419776001
6.999999999999991
0.004431848411938125
7.099999999999991
0.003266819056200014
7.19999999999999
0.0023840882014649163
7.29999999999999
0.0017225689390537363
7.39999999999999
0.0012322191684730624
7.499999999999989
8.726826950457925E-4
7.599999999999989
6.119019301137963E-4
7.699999999999989
4.247802705507695E-4
7.799999999999988
2.9194692579147323E-4
7.899999999999988
1.9865547139278204E-4
7.999999999999988
1.3383022576489198E-4
3-*
Mean and Standard Deviation
- Most common statistics used
- Mean or expected value
E(x) = SxiP(xi)
- Standard deviation
s(x) = [S [xi - E(x)]2P(xi)]0.5
s(x) = [S [xi - m]2/n-1]0.5
3-*
Z-Scores
- Standard Z-score
- Measures the number of standard deviations away from the mean
- Calculated as such:
- Look up Z value in table to find probability
Normal Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0
1
2
3
4
5
6
7
8
x
P(x)
Normal Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0
1
2
3
4
5
6
7
8
x
P(x)
mean = 4, std. dev. = 1
-1 std. dev.
+1 std. dev.
68% of values
m
=
x
i
å
n
Z
=
x
-
mean
SD
