Question

Find the probability and interpret the results. If​ convenient, use technology to find the probability. During a certain week the mean price of gasoline was ​$2.716 per gallon. A random sample of 38 gas stations is drawn from this population. What is the probability that the mean price for the sample was between ​$2.697 and ​$2.715 that​ week? Assume sigma= $0.049.

Answer 1

Given that mean price =2.716 and population standard deviation as,  = 0.049

Hence the probability between 2.697 and 2.715 is calculated by finding Z score at given values as

Z at 2.697

and Z at X=2.715

Hence P(2.697<X<2.715) =P(-2.39>Z>-0.126) the probability is computed using Z table given below as

=0.4483-0.0082

=0.44

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We were unable to transcribe this image

2.697 2.716 -0.39 0.049

2.715 2.716 -0.02 0.049

Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0,01 0.02 0.03 0.04 0.05 0,06 0.07 0.08 0.09 Z 0.0003 0,0003 0.0003 0.0003 0.5000 0.5398 0.5040 0.5239 -3.4 0.0003 0.0003 0.0003 0,0003 0.0003 0.0002 0,0 0.5080 0,5120 0.5160 0.5199 0.5279 0.5319 0.5359 0,0005 0,0005 0,0005 0,0004 0.1 0.5438 0.5636 -3.3 0,0004 0.0004 0.0004 0,0004 0.0004 0,0003 0.5478 0.5517 0.5557 0.5596 0.5675 0.5714 0.5753 -3.2 0.0007 0.0007 0.5793 0.0006 0.0006 0,0006 0,0006 0.0006 0.0005 0.0005 0,0005 0.2 0.5832 0.5871 0.5910 0.5948 0.5987 0,6026 0.6064 0.6103 0.6141 0.6255 0.6628 0.0009 0.6217 0.659 -3.1 0.0010 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.3 0.6179 0.6293 0.633 0.6368 0.6406 0.6443 0.6480 0.6517 -3.0 0.0013 .0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.4 0.6554 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.7054 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.5 0.6915 0.6950 0,6985 0.7019 0.7088 0.7123 0.7157 0.7190 0.7224 -2.8 0,0026 0,0025 0.0024 0.0023 0,0023 0.0022 0.0021 0.002 0.0020 0.0019 0.6 0.7257 0.7291 0,7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7704 0.7995 -2.7 0,0035 0,0034 0.0045 0.0033 0,0032 0.0031 0.0041 0.0030 0.0029 0.0028 0.0027 0,0026 0.7 0.7580 0.7611 0,7642 0.7939 0.7673 0.7734 0.8023 0.7764 0.7794 0.7823 0.7852 0.8133 -2.6 0.0047 0,0044 0,0043 0.0040 0.0039 0,0038 0.0037 0.0036 0.8 0.7881 0.7910 0.7967 0,8051 0.8078 0.8106 -2.5 0.8264 0.0062 0,0060 0,0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0,9 0.8159 0.8186 0.8212 0.8238 0.8289 0,8315 0.8340 0.8365 0.8389 -2.4 -2.3 0.0082 0,0080 0.0078 0,0075 0.0073 0.0071 0.0069 0,0068 0.0066 0.0064 1.0 0.8413 0,8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 -2.2 -2.1 1.2 1.3 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.01 16 0.0113 0.01 10 0.8849 0.8869 0,8888 0.8907 0,8925 0.8944 0.8962 0.8980 0,8997 0.9015 0.0174 0.0170 0.0179 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.9032 0.9049 0.9066 0,9082 0.9099 0.91 15 0.913 0.9147 0.9162 0.9177 -2.0 0.0228 0.0222 0.0217 0.0197 0.0192 0.9192 0.9222 0.9279 0.0212 0,0207 0.0202 0.0188 0.0183 1.4 0.9207 0,9236 0,9251 0.9265 0.9292 0,9306 0,9319 0.0287 0.0281 0.0274 1.5 0.9332 -1.9 0.0268 0,0262 0.0256 0.0250 0,0314 0,0392 0.0244 0,0239 0.0233 0.9345 0.9357 0,9370 0,9382 0.9394 0.9406 0.9418 0.9429 0,9441 0,0359 0.035 0.9452 0.9554 -1.8 0.0344 0.0336 0,0329 0.0322 0.0307 0.0301 0,0294 1.6 0.9463 0.9474 0.9573 0,9484 0.9495 0.9505 0.9515 0.9525 0,9535 0,9545 0.0427 1.7 -1.7 0.0446 0.0436 0.0418 0.0409 0.040 0.0384 0.0375 0.0367 0.9564 0.9582 0.9591 0.9599 0.9608 0.9616 0,9625 0,9633 0.0548 1.8 -1.6 0.0537 0.0526 0.0516 0.0505 0.0495 0,0485 0.0475 0.0465 0.0455 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0,9706 0.9761 -1.5 0.0643 1.9 0.0668 0.0655 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9767 -1.4 -1.3 2.0 2.1 0.9778 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 0.9772 0.9783 0,9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 -1.2 2.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 0.9861 0,9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 0.1271 0.1492 0.1335 0.1562 2.3 0.9893 -1.1 0.1357 0.1314 0.1292 0.1251 0.1230 0.1210 0.1190 0.1401 0.1170 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0031 0.9911 0.9913 0.9916 0.1515 0.1469 0.1446 0.1423 0.1379 0.9918 0.9922 0.9934 0.9936 -1,0 0.1587 0.1539 2.4 0.9920 0.9925 0.9927 0.9929 0.9932 0.994 0.9956 -0.9 0,1841 0.1814 0.1788 0.1762 0.2033 0.1736 0.2005 0.1711 0.1685 0.1660 0.1635 0.1611 2.5 0.9938 0.9940 0.9943 0.9957 0.9945 0.9959 0.9946 0.9948 0.9949 0.995 0.9952 -0.8 0.2119 0.2090 0.2061 0.1977 0.1949 0.1922 0.1894 0.1867 2.6 0.9953 0.9955 0.9960 0.9961 0.9962 0.9963 0.9964 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 -0.6 -0.5 -0.4 0.2743 2.8 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.245 0,9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0,9980 0.9981 0.3085 0.2877 2.9 3.0 0.9981 0.9987 0.3050 0.3015 0.2981 0,2946 0.2912 0.2843 0.2810 0.2776 0.9982 0.9982 0.9983 0,9984 0.9984 0.9985 0.9985 0,9986 0.9986 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.9987 0.9987 0,9988 0,9988 0,9989 0.9989 0,9989 0.9990 0,9990 0.9990 0.3745 0.3 -0.2 0.3821 0.3783 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 3.1 0.9991 0.9991 0.9991 0,9992 0.9992 0.9992 0.9992 0.9993 0,9993 3.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.9993 0.9993 0,9994 0,9994 0,9994 0.9994 0.9994 0.9995 0.9995 0,9995 -0.1 0.4602 0.5000 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0,9996 0,9997 0.9998 -0,0 0.4920 0,4761 0.4721 0.9997 0.9997 0.9997 0.9997 0.4960 0.4880 0.4840 0.4801 0.4681 0,4641 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 Note that the probabilities given in this table represent the area to the LEFT of the z-score The area to the RIGHT of a z-score = 1 - the area to the LEFT of the z-score