1. The final exam scores in a statistics class are normally distributed with a mean µ = 64 and standard deviation o = 3.5. Show your COMPLETE solution below. Shade the appropriate region. Find the area under: c) P(59 < x < 70) d) P( 68 < x < 75)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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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:
c) P(59 < x < 70)
d) P( 68 < x < 75)
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: c) P(59 < x < 70) d) P( 68 < x < 75)
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
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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