A random sample of size 49 is taken from a normal population having a mean of 70 and a standard deviation of 2. A second random sample of size 81 is taken from a different normal population having a mean of 55 and a standard deviation of 6. Find the probability that the sample mean computed from the 49 measurements will exceed the sample mean computed from the 81 measurements by at least 13.7 but less than 15.4. Assume the difference of the means to be measured to the nearest tenth. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is (Round to four decimal places as needed.)
A random sample of size 49 is taken from a normal population having a mean of 70 and a standard deviation of 2. A second random sample of size 81 is taken from a different normal population having a mean of 55 and a standard deviation of 6. Find the probability that the sample mean computed from the 49 measurements will exceed the sample mean computed from the 81 measurements by at least 13.7 but less than 15.4. Assume the difference of the means to be measured to the nearest tenth. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is (Round to four decimal places as needed.)
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:A random sample of size 49 is taken from a normal population having a mean of 70 and a standard deviation of 2. A
second random sample of size 81 is taken from a different normal population having a mean of 55 and a standard
deviation of 6. Find the probability that the sample mean computed from the 49 measurements will exceed the
sample mean computed from the 81 measurements by at least 13.7 but less than 15.4. Assume the difference of the
means to be measured to the nearest tenth.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
The probability is
(Round to four decimal places as needed.)
Transcribed Image Text:Areas under the Normal Curve
Areas under the Normal Curve
z
.00
.01
-3.4
0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009 0.0009
-3.0 0.0013 0.0013 0.0013 0.0012
-2.9 0.0019 0.0018 0.0018 0.0017
-2.8 0.0026 0.0025 0.0024 0.0023
-2.7 0.0035 0.0034 0.0033 0.0032
-2.6 0.0047 0.0045 0.0044 0.0043
-2.5 0.0062 0.0060 0.0059 0.0057
-2.4 0.0082 0.0080 0.0078 0.0075
-2.3 0.0107 0.0104 0.0102 0.0099
.02
.03
.05
.04
.06
.07
0.0003 0.0003
0.0003 0.0003
0.0004 0.0004 0.0004 0.0004
0.0006 0.0006 0.0006 0.0005
0.0008 0.0008 0.0008 0.0008
0.0012 0.0011 0.0011 0.0011
0.0016 0.0016 0.0015 0.0015
0.0023 0.0022 0.0021 0.0021
0.0031 0.0030 0.0029 0.0028
.08
.09
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
z
Z
.00
.01
.02
.03
.04
.05
.06
.07
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.3
0.4
-0.3 0.3821 0.3783 0.3745
2
.00
.01
0.0041 0.0040 0.0039 0.0038
0.0055 0.0054 0.0052 0.0051
0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
0.0096 0.0094 0.0091 0.0089 0.0087
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571
0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3
0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192
0.3707 0.3669 0.3632 0.3594 0.3557
0.3483 -0.3
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.02
.03
.04
.05
.06
.07
.08
.09
Z
0.0014 0.0014 -2.9
0.0020 0.0019 -2.8
0.0027 0.0026 2.7
0.0037 0.0036 -2.6
0.0049 0.0048 -2.5
0.5
0.0084 -2.3
0.0110 -2.2
0.0143 -2.1
2.7
0.2483 0.2451 -0.6
0.2810
0.2776 -0.5
0.3156
0.3520
0.3121 -0.4
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2
.00
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.6179 0.6217 0.6255
0.6293 0.6331
0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0.9783 0.9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878
0.9881 0.9884 0.9887 0.9890 2.2
2.3
0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
0.9965 0.9966 0.9967
0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992
0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.01
.02
.03
.04
.05
.06
.07
.08
.09
.08
.09
0.5319 0.5359 0.0
2
Z
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