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According to a survey in a country, 15% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of p, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. O A. Not normal becausens0.05N and np(1 - p) 2 10 O B. Approximately normal because ns0.05N and np(1- p) < 10 OC. Not normal because ns0.05N and np(1 - p)< 10 O D. Approximately normal because ns0.05N and np(1 - p) 2 10 Determine the mean of the sampling distribution of p. = (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p. OA = (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 300 adults, more than 19% do not own a credit card? The probability is O: (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in more than 19% not owning a credit card. (Round to the nearest integer as needed.) (c) What is the probability that in a random sample of 300 adults, between 14% and 19% do not own a credit card? The probability is. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in between 14% and 19% not owning a credit card. (Round to the nearest integer as needed.) (d) Would it be unusual for a random sample of 300 adults to result in 42 or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) O A. The result unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%.

According to a survey in a country, 15% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of p, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. O A. Not normal becausens0.05N and np(1 - p) 2 10 O B. Approximately normal because ns0.05N and np(1- p) < 10 OC. Not normal because ns0.05N and np(1 - p)< 10 O D. Approximately normal because ns0.05N and np(1 - p) 2 10 Determine the mean of the sampling distribution of p. = (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p. OA = (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 300 adults, more than 19% do not own a credit card? The probability is O: (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in more than 19% not owning a credit card. (Round to the nearest integer as needed.) (c) What is the probability that in a random sample of 300 adults, between 14% and 19% do not own a credit card? The probability is. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in between 14% and 19% not owning a credit card. (Round to the nearest integer as needed.) (d) Would it be unusual for a random sample of 300 adults to result in 42 or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) O A. The result unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 15E: Describe the standard normal distribution. What are its characteristics?
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Area Area Standard Normal Distribution Standard Normal Distribution 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 -3.4 -3.3 -3.2 0.0003 0.0005 0.0007 0.0010 0.0013 0.0003 0.0005 0.0007 0.0009 0.0013 0.0003 0.0004 0.0006 0.0003 0.0005 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0008 0.0011 0.0003 0.0004 0.0005 0.0003 0.0004 0.0005 0.0002 0.0003 0.0005 0.0 0.1 0.2 0.3 0.4 0.5000 0.5398 0.5793 0.5040 0.5438 0.5832 0.6217 0.6591 0.5080 0.5478 0.5871 0.5120 0.5517 0.5910 0.6293 0.6664 0.5160 0.5557 0.5948 0.6331 0.6700 0.5199 0.5596 0.5987 0.5239 0.5636 0.6026 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0.5359 0.5753 0.6141 0.0006 -3.1 -3.0 0.0008 0.0011 0.0007 0.0010 0.0009 0.0009 0.0008 0.0012 0.0008 0.0007 0.0010 0.6179 0.6554 0.6255 0.6628 0.6368 0.6736 0.6480 0.6844 0.6517 0.6879 0.0013 0.0012 0.0011 0.6406 0.6772 -29 -2.8 -2.7 0.0019 0.0026 0.0035 0.0047 0.0062 0.0018 0.0025 0.0034 0.0018 0.0024 0.0033 0.0017 0.0023 0.0032 0.0016 0.0023 0.0031 0.0016 0.0022 0.0030 0.0015 0.0021 0.0029 0.0015 0.0021 0.0028 0.0014 0.0020 0.0027 0.0037 0.0049 0.0014 0.0019 0.0026 0.6915 0.7257 0.7580 0.7881 0.8159 0.6950 0.7291 0.7611 0.7910 0.8186 0.6985 0.7324 0.7642 0.7939 0.8212 0.7019 0.7357 0.7673 0.7967 0.8238 0.7054 0.7389 0.7704 0.7995 0.8264 0.7088 0.7422 0.7734 0.7123 0.7454 0.7764 0.8051 0.8315 0.7157 0.7486 0.7794 0.7190 0.7517 0.7823 0.8106 0.8365 0.7224 0.7549 0.7852 0.5 0.6 0.7 -2.6 -2.5 0.0045 0.0060 0.0044 0.0059 0.0043 0.0057 0.0041 0.0055 0.0040 0.0054 0.0039 0.0052 0.0038 0.0051 0.0036 0.0048 0.8023 0.8289 0.8078 0.8340 0.8133 0.8389 0.8 0.9 0.0078 0.0102 0.0073 -2.4 -2.3 -2.2 0.0082 0.0107 0.0139 0.0080 0.0104 0.0136 0.0075 0.0099 0.0129 0.0071 0.0094 0.0122 0.0158 0.0202 0.0069 0.0091 0.0119 0.0068 0.0089 0.0116 0.0066 0.0087 0.0113 0.0146 0.0188 0.0064 0.0084 1.0 1.1 1.2 0.8413 0.8643 0.8849 0.9032 0.9192 0.8438 0.8665 0.8869 0.9049 0.9207 0.8461 0.8686 0.8888 0.8485 0.8708 0.8907 0.8508 0.8729 0.8925 0.8531 0.8749 0.8944 0.8554 0.8770 0.8962 0.8577 0.8790 0.8980 0.8599 0.8810 0.8997 0.8621 0.8830 0.9015 0.0096 0.0125 0.0162 0.0207 0.0132 0.0110 -2.1 -2.0 0.0179 0.0228 0.0174 0.0222 0.0170 0.0217 0.0166 0.0154 0.0197 0.0150 0.0143 0.0183 1.3 1.4 0.9066 0.9222 0.9082 0.9236 0.9099 0.9251 0.9131 0.9279 0.9147 0.9292 0.9162 0.9306 0.9177 0.9319 0.0212 0.0192 0.9115 0.9265 0.0287 0.0359 0.0446 0.0548 0.0668 0.0281 0.0351 0.0436 0.0537 0.0655 0.0274 0.0344 0.0427 0.0268 0.0336 0.0418 0.0262 0.0329 0.0409 0.0256 0.0322 0.0401 0.0495 0.0606 0.0250 0.0314 0.0392 0.0244 0.0307 0.0384 0.0239 0.0301 0.0375 0.0233 0.0294 0.0367 -1.9 1.5 1.6 1.7 1.8 1.9 0.9332 0.9452 0.9554 0.9345 0.9463 0.9564 0.9357 0.9474 0.9573 0.9656 0.9726 0.9370 0.9484 0.9582 0.9382 0.9495 0.9591 0.9394 0.9505 0.9599 0.9678 0.9744 0.9406 0.9515 0.9608 0.9418 0.9525 0.9616 0.9429 0.9535 0.9625 0.9441 0.9545 0.9633 0.9706 0.9767 -1.8 -1.7 -1.6 -1.5 0.0526 0.0643 0.0516 0.0630 0.0505 0.0618 0.0485 0.0594 0.0475 0.0582 0.0465 0.0571 0.0455 0.0559 0.9686 0.9750 0.9693 0.9756 0.9664 0.9641 0.9713 0.9649 0.9719 0.9671 0.9738 0.9699 0.9761 0.9732 0.0808 0.0968 0.1151 0.0749 0.0901 0.1075 0.1271 0.1492 0.0735 0.0885 0.1056 0.1251 0.1469 0.0721 0.0869 0.1038 0.1230 0.1446 0.0708 0.0853 0.1020 0.0694 0.0838 0.1003 -1.4 -1.3 0.0793 0.0951 0.1131 0.0778 0.0934 0.1112 0.0764 0.0918 0.1093 0.0681 0.0823 0.0985 0.9772 0.9821 0.9861 0.9778 0.9826 0.9864 0.9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 2.0 2.1 2.2 0.9783 0.9830 0.9868 0.9798 0.9842 0.9878 0.9803 0.9846 0.9881 0.9909 0.9931 0.9808 0.9850 0.9884 0.9812 0.9854 0.9887 0.9913 0.9934 0.9817 0.9857 0.9890 -1.2 -1.1 -1.0 0.1357 0.1587 0.1335 0.1562 0.1314 0.1539 0.1292 0.1515 0.1210 0.1423 0.1190 0.1401 0.1170 0.1379 0.9893 0.9918 2.3 0.9896 0.9920 0.9898 0.9922 0.9906 0.9929 0.9911 0.9932 0.9916 0.9936 2.4 -0.9 -08 -0.7 0.1841 0.2119 0.2420 0.2743 0.3085 0.1814 0.2090 0.2389 0.1788 0.2061 0.2358 0.1762 0.2033 0.2327 0.1736 0.2005 0.2296 0.2611 0.2946 0.1711 0.1977 0.2266 0.2578 0.2912 0.1685 0.1949 0.2236 0.1660 0.1922 0.2206 0.2514 0.2843 0.1635 0.1894 0.2177 0.1611 0.1867 0.2148 2.5 2.6 2.7 2.8 2.9 0.9938 0.9953 0.9965 0.9940 0.9955 0.9966 0.9941 0.9956 0.9967 0.9976 0.9982 0.9943 0.9957 0.9968 0.9977 0.9983 0.9945 0.9959 0.9969 0.9977 0.9984 0.9946 0.9960 0.9970 0.9978 0.9984 0.9948 0.9961 0.9971 0.9979 0.9985 0.9949 0.9962 0.9972 0.9951 0.9963 0.9973 0.9952 0.9964 0.9974 0.9981 0.9986 0.2643 0.2981 0.2546 0.2877 -0.6 0.2709 0.3050 0.2676 0.2483 0.2810 0.2451 0.2776 0.9974 0.9981 0.9975 0.9982 0.9979 0.9985 0.9980 0.9986 -0.5 0.3015 -0.4 0.3446 0.3821 0.3409 0.3783 0.3372 0.3745 0.3336 0.3707 0.3300 0.3669 0.3264 0.3632 0.3228 0.3594 0.3192 0.3557 0.3156 0.3520 0.3121 0.3483 3.0 3.1 0.9987 0.9990 0.9987 0.9991 A 0002 0.9987 0.9991 0.9988 0.9991 0.9988 0.9992 0.9989 0.9992 A 0004 0.9989 0.9992 0.9989 0.9992 0.9990 0.9993 0.9990 0.9993 -0.3 A4012 A0004 00004
Transcribed Image Text:Area Area Standard Normal Distribution Standard Normal Distribution 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 -3.4 -3.3 -3.2 0.0003 0.0005 0.0007 0.0010 0.0013 0.0003 0.0005 0.0007 0.0009 0.0013 0.0003 0.0004 0.0006 0.0003 0.0005 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0008 0.0011 0.0003 0.0004 0.0005 0.0003 0.0004 0.0005 0.0002 0.0003 0.0005 0.0 0.1 0.2 0.3 0.4 0.5000 0.5398 0.5793 0.5040 0.5438 0.5832 0.6217 0.6591 0.5080 0.5478 0.5871 0.5120 0.5517 0.5910 0.6293 0.6664 0.5160 0.5557 0.5948 0.6331 0.6700 0.5199 0.5596 0.5987 0.5239 0.5636 0.6026 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0.5359 0.5753 0.6141 0.0006 -3.1 -3.0 0.0008 0.0011 0.0007 0.0010 0.0009 0.0009 0.0008 0.0012 0.0008 0.0007 0.0010 0.6179 0.6554 0.6255 0.6628 0.6368 0.6736 0.6480 0.6844 0.6517 0.6879 0.0013 0.0012 0.0011 0.6406 0.6772 -29 -2.8 -2.7 0.0019 0.0026 0.0035 0.0047 0.0062 0.0018 0.0025 0.0034 0.0018 0.0024 0.0033 0.0017 0.0023 0.0032 0.0016 0.0023 0.0031 0.0016 0.0022 0.0030 0.0015 0.0021 0.0029 0.0015 0.0021 0.0028 0.0014 0.0020 0.0027 0.0037 0.0049 0.0014 0.0019 0.0026 0.6915 0.7257 0.7580 0.7881 0.8159 0.6950 0.7291 0.7611 0.7910 0.8186 0.6985 0.7324 0.7642 0.7939 0.8212 0.7019 0.7357 0.7673 0.7967 0.8238 0.7054 0.7389 0.7704 0.7995 0.8264 0.7088 0.7422 0.7734 0.7123 0.7454 0.7764 0.8051 0.8315 0.7157 0.7486 0.7794 0.7190 0.7517 0.7823 0.8106 0.8365 0.7224 0.7549 0.7852 0.5 0.6 0.7 -2.6 -2.5 0.0045 0.0060 0.0044 0.0059 0.0043 0.0057 0.0041 0.0055 0.0040 0.0054 0.0039 0.0052 0.0038 0.0051 0.0036 0.0048 0.8023 0.8289 0.8078 0.8340 0.8133 0.8389 0.8 0.9 0.0078 0.0102 0.0073 -2.4 -2.3 -2.2 0.0082 0.0107 0.0139 0.0080 0.0104 0.0136 0.0075 0.0099 0.0129 0.0071 0.0094 0.0122 0.0158 0.0202 0.0069 0.0091 0.0119 0.0068 0.0089 0.0116 0.0066 0.0087 0.0113 0.0146 0.0188 0.0064 0.0084 1.0 1.1 1.2 0.8413 0.8643 0.8849 0.9032 0.9192 0.8438 0.8665 0.8869 0.9049 0.9207 0.8461 0.8686 0.8888 0.8485 0.8708 0.8907 0.8508 0.8729 0.8925 0.8531 0.8749 0.8944 0.8554 0.8770 0.8962 0.8577 0.8790 0.8980 0.8599 0.8810 0.8997 0.8621 0.8830 0.9015 0.0096 0.0125 0.0162 0.0207 0.0132 0.0110 -2.1 -2.0 0.0179 0.0228 0.0174 0.0222 0.0170 0.0217 0.0166 0.0154 0.0197 0.0150 0.0143 0.0183 1.3 1.4 0.9066 0.9222 0.9082 0.9236 0.9099 0.9251 0.9131 0.9279 0.9147 0.9292 0.9162 0.9306 0.9177 0.9319 0.0212 0.0192 0.9115 0.9265 0.0287 0.0359 0.0446 0.0548 0.0668 0.0281 0.0351 0.0436 0.0537 0.0655 0.0274 0.0344 0.0427 0.0268 0.0336 0.0418 0.0262 0.0329 0.0409 0.0256 0.0322 0.0401 0.0495 0.0606 0.0250 0.0314 0.0392 0.0244 0.0307 0.0384 0.0239 0.0301 0.0375 0.0233 0.0294 0.0367 -1.9 1.5 1.6 1.7 1.8 1.9 0.9332 0.9452 0.9554 0.9345 0.9463 0.9564 0.9357 0.9474 0.9573 0.9656 0.9726 0.9370 0.9484 0.9582 0.9382 0.9495 0.9591 0.9394 0.9505 0.9599 0.9678 0.9744 0.9406 0.9515 0.9608 0.9418 0.9525 0.9616 0.9429 0.9535 0.9625 0.9441 0.9545 0.9633 0.9706 0.9767 -1.8 -1.7 -1.6 -1.5 0.0526 0.0643 0.0516 0.0630 0.0505 0.0618 0.0485 0.0594 0.0475 0.0582 0.0465 0.0571 0.0455 0.0559 0.9686 0.9750 0.9693 0.9756 0.9664 0.9641 0.9713 0.9649 0.9719 0.9671 0.9738 0.9699 0.9761 0.9732 0.0808 0.0968 0.1151 0.0749 0.0901 0.1075 0.1271 0.1492 0.0735 0.0885 0.1056 0.1251 0.1469 0.0721 0.0869 0.1038 0.1230 0.1446 0.0708 0.0853 0.1020 0.0694 0.0838 0.1003 -1.4 -1.3 0.0793 0.0951 0.1131 0.0778 0.0934 0.1112 0.0764 0.0918 0.1093 0.0681 0.0823 0.0985 0.9772 0.9821 0.9861 0.9778 0.9826 0.9864 0.9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 2.0 2.1 2.2 0.9783 0.9830 0.9868 0.9798 0.9842 0.9878 0.9803 0.9846 0.9881 0.9909 0.9931 0.9808 0.9850 0.9884 0.9812 0.9854 0.9887 0.9913 0.9934 0.9817 0.9857 0.9890 -1.2 -1.1 -1.0 0.1357 0.1587 0.1335 0.1562 0.1314 0.1539 0.1292 0.1515 0.1210 0.1423 0.1190 0.1401 0.1170 0.1379 0.9893 0.9918 2.3 0.9896 0.9920 0.9898 0.9922 0.9906 0.9929 0.9911 0.9932 0.9916 0.9936 2.4 -0.9 -08 -0.7 0.1841 0.2119 0.2420 0.2743 0.3085 0.1814 0.2090 0.2389 0.1788 0.2061 0.2358 0.1762 0.2033 0.2327 0.1736 0.2005 0.2296 0.2611 0.2946 0.1711 0.1977 0.2266 0.2578 0.2912 0.1685 0.1949 0.2236 0.1660 0.1922 0.2206 0.2514 0.2843 0.1635 0.1894 0.2177 0.1611 0.1867 0.2148 2.5 2.6 2.7 2.8 2.9 0.9938 0.9953 0.9965 0.9940 0.9955 0.9966 0.9941 0.9956 0.9967 0.9976 0.9982 0.9943 0.9957 0.9968 0.9977 0.9983 0.9945 0.9959 0.9969 0.9977 0.9984 0.9946 0.9960 0.9970 0.9978 0.9984 0.9948 0.9961 0.9971 0.9979 0.9985 0.9949 0.9962 0.9972 0.9951 0.9963 0.9973 0.9952 0.9964 0.9974 0.9981 0.9986 0.2643 0.2981 0.2546 0.2877 -0.6 0.2709 0.3050 0.2676 0.2483 0.2810 0.2451 0.2776 0.9974 0.9981 0.9975 0.9982 0.9979 0.9985 0.9980 0.9986 -0.5 0.3015 -0.4 0.3446 0.3821 0.3409 0.3783 0.3372 0.3745 0.3336 0.3707 0.3300 0.3669 0.3264 0.3632 0.3228 0.3594 0.3192 0.3557 0.3156 0.3520 0.3121 0.3483 3.0 3.1 0.9987 0.9990 0.9987 0.9991 A 0002 0.9987 0.9991 0.9988 0.9991 0.9988 0.9992 0.9989 0.9992 A 0004 0.9989 0.9992 0.9989 0.9992 0.9990 0.9993 0.9990 0.9993 -0.3 A4012 A0004 00004
According to a survey in a country, 15% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of p, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. A. Not normal because n<0.05N and np(1 - p) 2 10 B. Approximately normal because ns0.05N and np(1 - p) < 10 C. Not normal because ns0.05N and np(1- p)< 10 D. Approximately normal because n<0.05N and np(1 - p) 2 10 Determine the mean of the sampling distribution of p. (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p. (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 300 adults, more than 19% do not own a credit card? The probability is. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect (Round to the nearest integer as needed.) to result in more than 19% not owning a credit card. (c) What is the probability that in a random sample of 300 adults, between 14% and 19% do not own a credit card? The probability is (Round to four decimal places as needed.) Ine ret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in between 14% and 19% not owning a credit card. (Round to the nearest integer as needed.) (d) Would it be unusual for a random sample of 300 adults to result in 42 or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) OA. The result is unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%.
Transcribed Image Text:According to a survey in a country, 15% of adults do not own a credit card. Suppose a simple random sample of 300 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of p, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of p below. A. Not normal because n<0.05N and np(1 - p) 2 10 B. Approximately normal because ns0.05N and np(1 - p) < 10 C. Not normal because ns0.05N and np(1- p)< 10 D. Approximately normal because n<0.05N and np(1 - p) 2 10 Determine the mean of the sampling distribution of p. (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p. (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 300 adults, more than 19% do not own a credit card? The probability is. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 300 adults were obtained, one would expect (Round to the nearest integer as needed.) to result in more than 19% not owning a credit card. (c) What is the probability that in a random sample of 300 adults, between 14% and 19% do not own a credit card? The probability is (Round to four decimal places as needed.) Ine ret this probability. If 100 different random samples of 300 adults were obtained, one would expect to result in between 14% and 19% not owning a credit card. (Round to the nearest integer as needed.) (d) Would it be unusual for a random sample of 300 adults to result in 42 or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) OA. The result is unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%. O B. The result is not unusual because the probability that p is less than or equal to the sample proportion is which is less than 5%.
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