Exercise 3.18. Let X be a normal random variable with mean 3 and variance 4. (a) Find the probability P(2 < X < 6). (b) Find the value c such that P(X > c) = 0.33.
Exercise 3.18. Let X be a normal random variable with mean 3 and variance 4. (a) Find the probability P(2 < X < 6). (b) Find the value c such that P(X > c) = 0.33.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 9E
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Transcribed Image Text:Exercise 3.18. Let X be a normal random variable with mean 3 and variance
4.
(a) Find the probability P(2 < X < 6).
(b) Find the value c such that P(X > c) = 0.33.
Transcribed Image Text:Appendix E
Table of values for (x)
Q(x) = P(Z ≤ x) is the cumulative distribution function of the standard normal
random variable Z.
0.0
0.1
0.2
0.3
0.4
0.5
0.6 0.7257 0.7291
0.7 0.7580 0.7611
0.8 0.7881 0.7910
0.9 0.8159 0.8186 0.8212
1.0 0.8413 0.8438 0.8461
1.1 0.8643 0.8665 0.8686
0.8888 0.8907
1.3 0.9032 0.9049 0.9066 0.9082
1.4 0.9192 0.9207 0.9222 0.9236
0.9370
1.2 0.8849 0.8869
1.5
0.9332 0.9345 0.9357
1.6
0.9452 0.9463 0.9474
0.9484
0.00
0.01
0.02
0.03
0.04 0.05
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199
0.5398 0.5438 0.5478 0.5517 0.5557 0.5596
0.5793 0.5832 0.5871 0.5910 0.5948 0.5987
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406
0.6554 0.6591 0.6628 0.6664 0.6700
0.6915 0.6950 0.6985
0.7019 0.7054
0.7324 0.7357 0.7389
0.7642 0.7673 0.7704
0.7939 0.7967 0.7995
0.8238 0.8264
0.8485 0.8508
0.8708 0.8729
0.8925
0.9099
0.9251
0.9382
0.9495
0.9582
0.9591
0.9656 0.9664
0.9671
1.7
1.8 0.9641 0.9649
0.9719
0.9778
0.9633
0.9693 0.9699 0.9706
0.9761 0.9767
0.9812 0.9817
1.9 0.9713
0.9726 0.9732
0.9738 0.9744
0.9750 0.9756
2.0 0.9772
0.9783
0.9788
0.9793
0.9798 0.9803 0.9808
2.1 0.9821 0.9826
0.9830
0.9834
0.9838
2.2
0.9861 0.9864
0.9868
0.9871
0.9875
0.9842 0.9846 0.9850 0.9854 0.9857
0.9878 0.9881 0.9884 0.9887
0.9906 0.9909 0.9911 0.9913
0.9890
0.9893 0.9896 0.9898
0.9901 0.9904
0.9916
2.3
2.4 0.9918 0.9920
0.9925
0.9927
0.9929 0.9931 0.9932 0.9934
0.9936
0.9922
0.9938 0.9940 0.9941
2.5
0.9943
0.9945
0.9946
0.9948 0.9949 0.9951
0.9952
2.6
0.9957
0.9959
0.9960
0.9961 0.9962 0.9963 0.9964
2.7
0.9953 0.9955 0.9956
0.9965 0.9966 0.9967
0.9974 0.9975 0.9976
0.9968 0.9969
0.9970
0.9972 0.9973 0.9974
0.9971
0.9979 0.9979 0.9980 0.9981
2.8
0.9977 0.9977
0.9983 0.9984
2.9
0.9981 0.9982 0.9982
3.0
0.9978
0.9984 0.9985 0.9985 0.9986 0.9986
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989
0.9989 0.9990 0.9990
0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996
0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997
3.1
0.9997 0.9997 0.9997 0.9998
0.06
0.09
0.07
0.08
0.5279 0.5319 0.5359
0.5239
0.5636
0.6026 0.6064 0.6103
0.5675 0.5714
0.5753
0.6141
0.6443 0.6480
0.6517
0.6808 0.6844
0.6879
0.6736 0.6772
0.7088
0.7123 0.7157 0.7190 0.7224
0.7422 0.7454 0.7486 0.7517 0.7549
0.7734
0.7764
0.7852
0.8023 0.8051
0.8289 0.8315
0.8531 0.8554 0.8577 0.8599
0.7794 0.7823
0.8078 0.8106
0.8133
0.8340 0.8365
0.8389
0.8621
0.8749
0.8770 0.8790 0.8810
0.8830
0.8944
0.8962 0.8980 0.8997 0.9015
0.9115
0.9147 0.9162 0.9177
0.9131
0.9279 0.9292 0.9306 0.9319
0.9265
0.9394
0.9406 0.9418 0.9429
0.9441
0.9505
0.9515 0.9525 0.9535 0.9545
0.9554 0.9564 0.9573
0.9608 0.9616 0.9625
0.9599
0.9678 0.9686
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