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111e graph of the waiting time (in seconds} at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled (a)(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. (a) (b) (G) g,- P a.- P i a: P i _ 2.- P i g 0.04 00:11:!" g 04 (51-51823- 004 {1'3 - 1P9 g 0.04 [51:12% E' Bil-1R :3 \"iix g7 - 31952.3 g =; 0:\" D 50 E/l' 0:\" D 50 E/l' in -20- 50 E/l' 0:\" D 50 E/l' Tima (ii see.) Time (ii sac.) rm; {in SELL] Tima (ii aa-c.) Graph '3' most closely resembles the sampling distribution of the sample means, because \"i = I], a; = I] and the graph r is the same shape as the graph for the original distribution approximates a normal curve 111e graph of the annual snowrall distribution (in feet) for a particular county is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Determine which of the graphs labeled (ch) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. smwran rm fae Choose the correct graph below. -:j::- A. - 2191'3. '11:: c. PEX) 9' 0' =2.4 Q p!- = 3.5 X _ X E.' --214?1013 0246510 -2 1 snow-rail :'n feet: Snowfall rm feet: SmMall rm rest: 111is graph most closely resembles the sampling distribution of the sample means, because \"i = I], a; = I] and the graph approximates a normal curve. The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 65, find the probability of a sample mean being less than 20.1 if u = 20 and o = 1.33. Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table. For a sample of n = 65, the probability of a sample mean being less than 20.1 if u = 20 and o = 1.33 is (Round to four decimal places as needed.) - X Standard Normal Table (Page 1) Standard Normal Table (Page 2) Area Area 0 .06 .07 .09 .09 .08 .07 .0 .04 .03 .0 .01 .03 .05 .08 .01 .00 Z .00 .02 .04 .5040 .508 .5120 .5199 5239 .5279 .5319 .5359 3.4 .0002 .0003 .0003 .0003 .0003 10003 5160 .0003 .0003 .0003 0003 0.0 5000 .0004 .0004 .0005 .0005 .0005 0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 5714 .5753 - 3.3 .0003 .0004 .0004 .0004 0004 .0007 0.2 .5793 5832 5871 .5910 .5948 5987 6064 .6103 .6141 - 3.2 0005 .0005 0005 0006 .0006 0006 0006 0006 0007 .6026 .6255 6331 6368 .6406 6443 6480 6517 - 3.1 .0007 0007 0008 .0008 0008 10008 .0009 0009 .0009 .0010 0.3 6179 6217 .6293 6700 .6736 6808 .6844 6879 - 3.0 .0010 0010 0011 001 .0011 0012 .0012 6772 0013 0013 0013 0.4 6554 6591 .6628 .6664 7088 7123 .7157 .7190 - 2.9 0014 .0014 0015 0015 0016 0016 0017 0018 0018 0019 0.5 6915 6950 .6985 .7019 .7054 7224 0 19 0021 0021 .0022 0023 0023 0024 .0025 0026 0.6 .7257 .7291 .7324 .7357 .7389 ./422 7454 .7486 .7517 7549 - 2.8 0020 .7704 .7734 .7764 .7794 .7823 7852 - 2.7 0026 0027 0028 0029 .0030 0031 .0032 0033 0034 0035 0.7 .7580 .7611 7642 .7673 7939 .7967 .7995 8023 8051 8078 .8106 .8133 - 2.6 .0036 0037 0038 .0039 .0040 10041 .0043 0044 .0045 0047 0.8 7881 7910 0.9 8186 .8212 .8238 8264 8289 8315 .8340 .8365 .8389 -2.5 0048 0049 0051 0057 0054 0055 0057 .0059 .0060 0062 8159 8531 8577 8599 .8621 - 2.4 0066 0068 0069 .0071 0073 .0075 .0080 .0082 1.0 8413 3438 .8461 .8485 8508 8554 0099 .0102 .0104 0107 1.1 8643 8665 .8686 .8708 8729 8749 8770 .8790 8810 .8830 - 2.3 .0084 0087 .0089 .0091 .0094 10096 8869 8907 .8925 8944 8962 .8980 8997 .9015 - 2.2 .0110 0113 0116 0119 .0122 0125 0129 .0132 .0136 0139 1.2 8849 .8888 1.3 9032 9049 9066 .9082 .9099 915 9131 9147 9162 9177 - 2.1 .0143 0146 150 0154 .0158 0162 D160 .0170 .0174 0179 0188 0192 .0197 .0202 0307 0212 .0217 .0222 0228 1.4 9192 9207 .9222 .9236 .9251 .9265 .9279 9292 9306 .9319 -2.0 .0183 0287 1.5 9332 9345 9357 .9370 .9382 9394 9406 9418 9429 9441 - 1.9 .0233 .0239 0244 .0250 .0256 10262 0268 0274 .0281 9463 .0322 10329 0336 0344 0351 0359 1.6 9452 9474 .9484 .9495 9505 9515 9525 9535 .9545 - 1.8 .0294 .0301 0307 .0314 0397 0401 0409 0418 .0427 0436 0446 1.7 9554 2564 .9573 .9582 9591 .9599 .9608 9616 9625 .9633 - 1.7 .0367 0375 0384 0465 .0495 0505 0516 0526 0537 0548 1.8 9641 649 9656 .9664 .9671 9678 .9686 9693 9699 .9706 - 1.6 0475 719 .9726 .9732 9738 .9744 .9750 9756 .9761 .9767 -1.5 .0559 .0571 0582 .0594 .0606 0618 0630 .0643 .0655 0668 1.9 9713 2.0 9772 778 .9783 9788 9793 .9798 9803 9808 .9812 .9817 - 1.4 .0681 0694 0708 0721 .0735 10749 .0764 .0778 .0793 0808 2.1 9821 826 9830 .9834 9838 9842 9846 9850 9854 9857 - 1.3 .0823 0838 0853 0869 .0885 0901 .0918 .0934 .0951 .0968 .9871 9875 .9878 9881 9884 9887 .9890 - 1.2 0965 .1003 1020 .1038 .1056 1075 .1093 .1112 .1131 .1 151 2.2 9861 864 .9868 9898 9904 .9906 .9909 9911 .9913 9916 - 1.1 ,1170 1190 1210 .123 .1251 .1271 .1292 .1314 .1335 1357 2.3 .9893 9896 .9901 .1587 2.4 9918 9920 9922 9925 9927 9929 .9931 9932 9934 9936 - 1.0 .1379 1401 1423 144 .1469 .1492 1515 .1539 .1562 .9941 9945 9946 .9948 .9949 .9951 .9952 -0.9 1611 .1635 1660 .1685 .1736 .1762 1788 .1814 .1841 2.5 .9938 9940 .9943 .1711 9956 2033 .2090 2119 2.6 .9953 955 .9957 9959 9960 9961 9962 .9963 .9964 -0.8 180/ 1894 1922 1949 1977 2005 2061 1966 9967 .9968 .9969 .9970 9971 9972 .9973 .9974 -0.7 .2148 2177 .2206 .2236 .2266 .2296 .2327 .2358 .2389 .2420 2.7 9965 .9977 9977 9978 .9979 9979 9980 9981 -0.6 2451 2483 2514 .2546 .2611 .2643 .2709 .9974 9975 9976 .2578 .2676 2743 2.8 2.9 9981 9982 9982 9983 9984 9984 .9985 9985 9980 9986 -0.5 .2776 2810 2843 2877 .2912 2946 .2987 .3015 .3050 3085 3.0 9987 9987 9987 .9988 .9988 9989 9989 9989 9990 9990 -0.4 3121 3156 .3192 .3228 3264 .3300 .3336 .3372 .3409 .3446 3821 3.1 .9990 9991 9991 9991 .9992 .9992 .9992 .9992 9993 .9993 -0.3 3483 .3520 35 57 3594 3632 .3669 .370 .3745 .3783 9993 9994 9994 9994 .9994 9995 9995 .9995 - 0.2 .3859 .3897 .3936 .3974 4013 4052 .4090 .4129 4168 4207 3.2 .9993 9994 4602 3.3 9995 4522 4562 .9995 9995 9996 9996 9996 .9996 .9996 09 96 9997 -0.1 4247 .4286 4325 4364 4404 4143 .4483 .9997 .9997 .9998 -0.0 4641 4681 4721 .4761 4801 4840 4880 4920 4960 5000 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .08 .09 .09 .08 .07 .06 .05 .04 .03 02 -01 .00 .00 .01 .02 .03 .04 .05 .06 .07