1. The final exam scores in a statistics class are normally distributed with a mean u = 64 and standard deviation o = 3.5. Show your COMPLETE solution below. Shade the appropriate region. Find the area under: a) P(x < 56) b) P(x > 50) c) P(59 < x < 70)
1. The final exam scores in a statistics class are normally distributed with a mean u = 64 and standard deviation o = 3.5. Show your COMPLETE solution below. Shade the appropriate region. Find the area under: a) P(x < 56) b) P(x > 50) c) P(59 < x < 70)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Transcribed Image Text:1. The final exam scores in a statistics class are normally distributed with a mean u = 64 and
standard deviation o = 3.5. Show your COMPLETE solution below. Shade the appropriate region.
Find the area under:
a) P(x < 56)
b) P(x > 50)
c) P(59 < x < 70)
Transcribed Image Text:STANDARD NORMAL TABLE (Z)
Entries in the table give the area under the curve
between the mean and z standard deviations above
the mean. For example, for z = 1.25 the area under
the curve between the mean (0) and z is 0.3944.
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.0000
0.0040 0.0080 0.0120 0.0160
0.0190 0.0239 0.0279 0.0319 0.0359
0.1
0.0398 0.0438
0.0478
0.0517 0.0557 0.0596
0.0636
0.0675
0.0714 0.0753
0.2 0.0793 0.0832 0.0871
0.0910 0.0948
0.0987
0.1026
0.1064
0.1103 0.1141
0.3
0.1179
0.1217 0.1255 0.1293
0.1331
0.1368 0.1406
0.1443
0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664
0.5 0.1915 0.1950 0.1985
0.6 0.2257 0.2291 0.2324
0.7
0.8
0.1700 0.1736 0.1772 0.1808
0.1844 0.1879
0.2019 0.2054
0.2088
0.2123 0.2157 0.2190 0.2224
0.2357 0.2389
0.2422
0.2454
0.2486
0.2517 0.2549
0.2580 0.2611
0.2642 0.2673 0.2704 0.2734 0.2764
0.2794
0.2823 0.2852
0.2881
0.2910 0.2939 0.2969 0.2995 0.3023
0.3051
0.3078
0.3106 0.3133
0.9
0.3159
0.3186
0.3212
0.3238 0.3264
0.3289
0.3315
0.3340
0.3365 0.3389
1.0
1.1
0.3413
0.3438 0.3461
0.3485
0.3508
0.3513
0.3554
0.3577
0.3529 0.3621
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.3770 0.3790
0.3810 0.3830
1.2
0.3849
0.3869
0.3888
0.3907 0.3925
0.3944
0.3962 0.3980
0.3997 0.4015
1.3
1.4
1.5
0.4032
0.4049 0.4066
0.4082 0.4099 0.4115 0.4131
0.4147 0.4162 0.4177
0.4192
0.4207 0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306 0.4319
0.4332 0.4345
0.4357 0.4370 0.4382
0.4394
0.4406
0.4418
0.4429 0.4441
1.6
0.4452
0.4463 0.4474
0.4484
0.4495 0.4505
0.4515 0.4525
0.4535 0.4545
1.7 0.4554
0.4564 0.4573 0.4582 0.4591
0.4599
0.4608
0.4616
0.4625 0.4633
1.8
1.9
0.4641
0.4649 0.4656 0.4664
0.4671
0.4678 0.4686
0.4693
0.4699 0.4706
0.4713 0.4719
0.4726
0.4732 0.4738 0.4744
0.4750 0.4756
0.4761
0.4767
2.0
0.4772
0.4778 0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
2.1
0.4821
0.4826 0.4830 0.4834
0.4838 0.4842 0.4846
0.4850
0.4854 0.4857
2.2
2.3
2.4
0.4861
0.4864
0.4868 0.4871
0.4875 0.4878
0.4881
0.4884
0.4887
0.4890
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909 0.4911
0.4913
0.4916
0.4918
0.4920
0.4922
0.4925 0.4927 0.4929
0.4931
0.4932
0.4934 0.4936
2.5
2.6 0.4953
0.4938
0.4940 0.4941
0.4943 0.4945 0.4946
0.4948 0.4949
0.4951
0.4952
0.4955
0.4956
0.4957 0.4959
0.4960
0.4961
0.4962
0.4963 0.4964
2.7
2.8 0.4974
2.9
3.0
3.1
3.2 0.4993 0.4993 0.4994 0.4994
3.3 0.4995 0.4995 0.4995
3.4
0.4965
0.4966 0.4967
0.4968
0.4969
0.4970
0.4971
0.4972
0.4973 0.4974
0.4975 0.4976 0.4977 0.4977 0.4978
0.4979
0.4979
0.4980 0.4981
0.4981
0.4982 0.4982
0.4983
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
0.4987 0.4987
0.4987
0.4988
0.4988 0.4989
0.4989 0.4989
0.4990 0.499o
0.4990 0.4991
0.4991
0.4991
0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
0.4994
0.4994 0.4994 0.4995 0.4995 0.4995
0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
0.4997 0.4997 0.4997
0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
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