5. (6 pts.) The monthly utility bills in a certain city are normally distributed, with a mean of $100 and a standard deviation of $12. A utility bill is randomly selected. Draw a normal curve as part of your work. a. Find the probability the bill is less than 580. b. Find the probability the bill is more than $115. c. What percent of people in this city spend between $75 and $95 on utilities? 6. (6 pts. each) The weights of adult male rhesus monkeys are normally distributed, with a mean of 15 pounds and a standard deviation of 3 pounds. Draw a normal curve as part of your work. a. Find the probability one randomly selected monkey weighs between 13 and 17 pounds. b. What percent of monkeys weigh more than 20 pounds? c. What is the weight of a monkey that is at the maximum value of the lowest 25% of rhesus monkeys? 7. (6 pts.) What z-score is equal to P46? Draw a normal curve as part of your work. 8. (6 pts.) What z-score is equal to 20.06' Draw a normal curve as part of your work. 9. (6 pts. each) A manufacturer claims that the mean weight of ice cream cartons is 10 ounces with a standard deviation of 0.5 ounces. Assume the weights are normally distributed. You test 32 cartons and find their mean weight is 10.17 ounces. Draw a normal curve as part of your work. a. Assuming the manufacturer's claim is correct, what is the probability that the mean of the sample of 32 cartons is 10.17 ounces or more? b. Using your answer from part a., what do you think of the manufacturer's claim? Explain. 1. (6 pts. each) Find the area of the shaded region under each standard normal curve shown below. a. b. z=-1.B z=0.1 2:2.15 3. ( 6 pts. each) For each problem below assume the data comes from a normal distribution, sketch a graph, then nd the indicated probability. a. Less than 2 = 1.28 b. Between 2 = 0.5 and z = 1.5. 4. (6 pts. each) The area of a shaded region under a standard normal curve is indicated. Find the zscore. a. b. 0.6255 0.0162 0 z 0 z POSITIVE z Scores TABLE A-2 (continued) Cumulative Area from the LEFT .06 .07 08 09 00 .01 .02 .03 04 05 5319 5359 5040 .5080 .5120 5160 5199 5239 .5279 0.0 .5000 .5714 5753 5438 5478 .5517 .5557 5596 -.5636 .5675 0.1 .5398 6141 .5910 .5948 .5987 .6026 .6064 .6103 0.2 .5793 5832 5871 .6443 6480 6517 6406 .6179 6217 .6255 .6293 .6331 .6368 0.3 .6879 .6628 .6664 6700 .6736 .6772 .6808 .6844 0.4 .6554 6591 7224 .7019 .7054 .7088 .7123 .7157 .7190 0.5 .6915 6950 6985 7454 .7486 .7517. .7549 0.6 .7257 7291 7324 7357 .7389 .7422 7764 .7794 .7852 .7734 7823 0.7 .7580 7611 7642 .7673 .7704 .8051 .8078 8106 8133 .7910 7967 .7995 0.8 7881 .7939 8023 .8315 .8340 .8365 8389 8289 0.9 .8159 8186 .8212 .8238 .8264 .8554 .8577 .8599 8621 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8729 .8749 8770 .8790 .8810 8830 1.1 .8643 8665 .8686 .8708 9015 8907 .8925 8944 .8962 .8980 8997 1.2 .8849 8869 .8888 .9162 .9177 .9049 .9066 .9082 .9099 9115 .9131 .9147 .9032 9279 .9292 .9306 9319 .9192 .9207 .9222 .9236 .9251 9265 9441 9345 .9382 9394 9406 9429 9332 9357 .9370 .9418 .9535 .9545 .9452 9463 9474 .9484 .9495 9505 9515 .9525 9599 .9608 .9616 9625 9633 .9554 9564 9573 .9582 .9591 .9686 .9693 .9699 9706 .9656 .9671 9678 1.8 .9641 .9649 .9664 .9761 .9767 9713 9719 9726 .9732 .9738 9744 9750 .9756 1.9 .9793 9803 .9808 9812 9817 .9772 9778 9783 .9788 9798 9842 9846 .9850 .9854 3857 .9821 .9826 .9830 9834 .9838 9878 9881 9884 9887 9890 9861 9864 9868 9871 9875 9909 .9911 9913 .9916 .9893 9896 .9898 .9901 .9904 9906 9931 .9932 .9934 .9936 .9925 9929 .9918 .9920 - .9922 .9927 .9943 .9945 9946 .9948 .9949 .9951 9952 .9938 .9940 .9941 .9963 .9964 ..9955 .9956 .9957 .9959 .9960 .9961 .9962 .9953 .9973 .9974 .9965 9966 .9967 .9968 9969 9970 .9971 .9972 2.7 .9979 .9980 .9981 2.8 .9974 .9975 .9976 .9977 9977 .9978 6466' .9984 .9985 .9985 .9986 9986 2.9 .9981 9982 .9982 .9983 9984 9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 3.0 9987 .9987 9992 .9992 .9993 9993 .9990 9991 .9991 .9991 9992 .9992 3.1 .9994 .9994 .9995 .9995 9995 3.2 .9993 .9993 .9994 $666' .9994 .9996 .9996 .9996 .9996 .9996 .9996 9997 3.3 .9995 .9995 .9995 9997 .9997 9997 9997 9997 9997 9998 3.4 9997 9997 .9997 3.50 and up 9999 Common Critical Values NOTE: For values of z above 3.49, use 0.9999 for the area. Confidence Critica Use these common values that result from interpolation: Level Value 0.90 1.645 z score Area 0.95 1.96 1.645 0.9500 0.99 2.575 ).9950 2.575NEGATIVE z Scores Z 0 TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT .0 .07 .08 .09 .00 .02 03 .04 .05 .01 -3.50 and lower .0001 .0003 0003 .0003 .0003 0003 .0003 0002 -3.4 .0003 .0003 .0003 .0004 .0004 .0004 0004 .0004 .0003 -3.3 .0005 .0005 .0005 .0004 0007 0006 .0006 0006 0006 .0006 0005 .0005 0005 -3.2 .0007 0009 .0009 0008 0008 .0008 0008 0007 0007 -3.1 .0010 0009 0013 .0012 0012 0011 .0011 0011 .0010 .0010 -3.0 .0013 0013 .0015 0015 .0014 .0014 -2.9 .0019 0018 0018 .0017 0016 .0016 0025 0024 .0023 0023 .0022 .0021 0021 0020 .0019 -2.8 .0026 0028 .0027 0026 -2.7 .0035 0034 .0033 .0032 0031 .0030 .0029 0045 .0044 .0043 0041 .0040 .0039 0038 .0037 0036 -2.6 .0047 .0059 .0057 0055 .0054 .0052 0051 .0049 .0048 -2.5 .0062 .0060 .0066 .0064 -2.4 .0082 0080 .0078 .0075 .0073 .0071 .0069 .0068 .0094 .0091 .0089 .0087 0084 -2.3 .0107 .0104 .0102 .0099 .0096 0110 .0139 0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 -2.2 .0158 .0154 .0150 .0146 0143 -2.1 .0179 0174 .0170 .0166 .0162 .0188 .0183 -2.0 .0228 0222 .0217 .0212 .0207 .0202 .0197 0192 .0274 .0268 0262 .0256 .0250 0244 .0239 .0233 -1.9 .0287 0281 .0294 -1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 0307 .0301 0367 .0446 0436 .0427 .0418 0409 .0401 .0392 0384 .0375 -1.7 .0495 .0485 .0475 .0465 .0455 0505 -1.6 .0548 0537 .0526 .0516 .0630 0618 .0606 .0594 .0582 .0571 .0559 -1.5 .0668 0655 .0643 .0735 .0721 .0708 .0694 .0681 -1.4 .0808 0793 .0778 .0764 0749 0823 0951 .0934 .0918 0901 .0885 .0869 0853 .0838 -1.3 .0968 1075 .1056 .1038 1020 .1003 .0985 -1.2 .1151 1131 .1112 1093 1271 .1251 .1230 1210 .1190 1170 -1.1 .1357 1335 .1314 .1292 1423 .1401 1379 -1.0 .1587 1562 .1539 .1515 1492 .1469 .1446 .1736 .1711 .1685 1660 .1635 .1611 -0.9 1841 .1814 . 1788 .1762 .2061 .2033 2005 .1977 .1949 1922 .1894 1867 -0.8 .2119 2090 2358 .2327 2296 .2266 2236 2206 2177 2148 -0.7 .2420 2389 .2743 2709 2676 .2643 2611 .2578 2546 2514 2483 2451 -0.6 2810 2776 -0.5 3085 3050 .3015 .2981 2946 2912 2877 2843 .3336 .3300 .3264 .3228 .3192 .3156 3121 -0.4 .3446 3409 .3372 3632 3594 3557 .3520 .3483 -0.3 .3821 3783 .3745 .3707 .3669 .4013 3974 3936 .3897 3859 .4052 -0.2 4207 4168 .4129 .4090 4286 4247 -0.1 .4602 4562 4522 .4483 4443 4404 4364 4325 4840 4801 476 .4721 .468 464 -00 5000 4960 4920 .4880 (continued) NOTE: For values of z below -3.49, use 0.0001 for the area. "Use these common values that result from interpolation: z Score Area 0.0500 -2.575 0.0050