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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 Ib and 171 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.4 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 lb. The probability is approximately (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 171 lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a sample of pilots is more important. O B. Part (a) because the seat performance for a single pilot is more important. OC. Part (b) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 Ib and 171 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.4 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 lb. The probability is approximately (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 171 lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a sample of pilots is more important. O B. Part (a) because the seat performance for a single pilot is more important. OC. Part (b) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 Ib and 171 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.4 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 Ib. The probability is approximately (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 Ib and 171 lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a sample of pilots is more important. O B. Part (a) because the seat performance for a single pilot is more important. OC. Part (b) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important.
Transcribed Image Text:An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 Ib and 171 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.4 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 Ib. The probability is approximately (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 Ib and 171 lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a sample of pilots is more important. O B. Part (a) because the seat performance for a single pilot is more important. OC. Part (b) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important.
Standard Normal (z) Distribution: Cumulative Area from the LEFT Standard Normal (2) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 04 .05 .06 .07 .08 09 00 .01 02 0 04 05 06 07 .09 0.0 5000 5040 5080 5120 5160 5199 5239 5279 .5319 5359 -3.50 and lower 0.1 5398 5438 5478 .5517 .5557 .5596 5636 5675 .5714 .5753 0001 0.2 5793 5832 5871 5910 .5948 5987 .6026 .6064 .6103 .6141 -14 0003 .0003 .0003 0003 .0003 0003 .0003 0003 0003 0002 0.3 6179 6217 6255 .6293 .6331 6368 6406 .6443 .6480 6517 -13 0005 .0005 .0005 0004 .0004 0004 .0004 0004 0004 0003 0.4 6554 6591 6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 -32 0007 .0007 .0006 0006 .0006 0006 .0006 0005 0005 .0006 0.5 6915 6950 .6985 7019 .7054 7088 .7123 7157 .7190 7224 -1.1 0010 .0009 .0009 0009 .0008 0008 .0008 0008 D007 .0007 -3.0 0013 .0013 .0013 0012 .0012 0011 0.6 7257 7291 7324 7357 7389 7422 .7454 .7486 .7517 7549 0011 .0011 0010 .0010 -29 0019 .0018 .0018 0017 .0016 0016 .0015 0015 0014 0014 0.7 7580 7611 7642 7673 7704 7734 7764 7794 .7823 7852 -2.8 0026 .0025 .0024 0023 .0023 .0022 .0021 0021 0020 .0019 0.8 .7881 7910 7939 7967 7995 8023 B051 8078 8106 8133 -2.7 0036 .0034 .0033 .0032 .0001 0030 .0029 0028 0027 0026 0.9 .8159 8186 8212 .8238 8264 8289 B315 8340 8365 8389 -2.6 0047 .0045 .0044 .0043 .0041 0040 .0039 0038 0037 .0036 1.0 .8413 8438 8461 8485 8508 .8531 B564 8577 8599 8621 -25 0062 .0060 .0069 0057 .0065 0064 .0052 0051 0049 .0048 1.1 8643 8665 8686 8708 8729 8749 8770 8790 8810 8830 .0089 -24 -2.3 0082 .0080 .0078 0075 .0073 0071 .0064 1.2 8849 8869 8888 8907 8925 8944 8962 8980 8997 9015 0107 .0104 .0102 0099 .0096 0094 .0091 0089 0087 .0084 1.3 9032 9049 9066 9082 9099 9115 9131 9147 .9162 9177 -22 0139 .0136 .0132 .0129 .0125 0122 .0119 0116 0113 0110 1.4 9192 9207 9222 9236 9251 9265 9279 9292 9306 9319 -2.1 0179 .0174 .0170 0166 .0162 0158 .0154 0150 0146 .0143 1.5 9332 .9345 .9357 9370 9382 9394 9406 9418 9429 9441 -2.0 0228 .0222 .0217 .0212 .0207 .0202 .0197 0192 0188 0183 1.6 9452 9463 .9474 9484 9495 9505 9515 9525 9535 9545 -1.9 0287 .0281 .0274 .0268 .0262 0256 .0250 0244 0229 .0233 1.7 .9554 9564 .9573 9582 .9591 9599 9608 9616 .9625 9633 -1.8 0359 .0361 .0344 0336 .0329 0322 .0314 .0301 .0294 -1.7 0446 .0436 .0427 .0418 .0409 0401 .0392 0384 0375 .0367 1.8 9641 9649 .9656 9664 9671 9678 9686 9693 9699 9706 -1.6 0548 .0537 0626 0516 .0505 0496 .0485 0475 0465 0455 1.9 9713 9719 9726 9732 9738 9744 9750 9756 9761 9767 -1.5 0688 .0666 .0843 0630 .0618 0606 .0594 0682 0671 0669 2.0 .9772 .9778 .9783 9788 9793 .9798 9803 9808 9812 9817 -1.4 0808 .0793 .0778 0764 .0749 .0735 .0721 0708 O694 0681 2.1 9821 9826 9830 9834 9838 9842 9846 9850 9854 9857 -13 0968 0951 0934 .0918 .0901 0885 .0889 0853 0838 0823 2.2 9861 9864 .9868 9871 9875 9878 9881 9884 9887 9890 -12 .1151 .1131 .1112 .1093 .1075 1056 1038 1020 1003 0985 2.3 .9893 .9896 .9898 9901 9904 9906 9909 9911 9913 9916 -1.1 .1357 1336 .1314 1292 .1271 .1251 .1230 1210 .1190 .1170 2.4 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 1446 1423 .1401 .1379 2.5 9938 9940 .9941 9943 9945 9946 9948 9949 9951 9952 -0.9 1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 2.6 9953 9955 .9956 9957 9959 9960 9961 9962 9963 9964 -0.8 2119 2090 2061 2033 2006 .1977 1949 1922 .1894 .1867 2.7 9965 9966 .9967 9968 9969 9970 9971 9972 9973 9974 -07 -0.6 2420 2389 2358 2327 .2296 2266 2236 2206 2177 .2148 2743 2709 2676 2643 .2611 2578 .2546 2514 2483 .2461 2.8 9974 .9975 .9976 9977 9977 9978 9979 9979 9980 .9981 9982 9982 9983 9988 -0.5 3086 3060 3015 2981 .2946 2912 2877 2843 2810 2776 2.9 9981 9984 9984 9985 9985 9986 9986 -04 3446 3409 .3372 3336 3300 3264 3228 3192 3156 .3121 3.0 9987 9987 9987 9988 9989 9989 9989 9990 9990 -03 3821 3703 .3745 3707 .3689 3632 3594 3567 3620 3483 3.1 9990 9991 .9991 9991 9992 9992 9992 9992 9993 9993 4207 4168 A129 A090 A052 4013 2974 2936 3897 3859 9995 9996 -02 3.2 9993 9993 9994 9994 9994 9994 9994 9995 9995 -01 4602 4662 A522 4483 A443 4404 4364 4325 A286 4247 9996 9997 3.3 9995 9995 9995 9996 9996 9996 9996 9997 -00 5000 4960 A920 4880 AB40 4801 .4761 4721 4681 4641 3.4 9997 9997 .9997 .9997 3997 9997 9997 .9997 9998 3.50 and up 00 .01 .02 02 04 05 06 07 08 09 9999 .00 .01 .02 .03 04 05 .06 .07 .08 09
Transcribed Image Text:Standard Normal (z) Distribution: Cumulative Area from the LEFT Standard Normal (2) Distribution: Cumulative Area from the LEFT .00 .01 .02 .03 04 .05 .06 .07 .08 09 00 .01 02 0 04 05 06 07 .09 0.0 5000 5040 5080 5120 5160 5199 5239 5279 .5319 5359 -3.50 and lower 0.1 5398 5438 5478 .5517 .5557 .5596 5636 5675 .5714 .5753 0001 0.2 5793 5832 5871 5910 .5948 5987 .6026 .6064 .6103 .6141 -14 0003 .0003 .0003 0003 .0003 0003 .0003 0003 0003 0002 0.3 6179 6217 6255 .6293 .6331 6368 6406 .6443 .6480 6517 -13 0005 .0005 .0005 0004 .0004 0004 .0004 0004 0004 0003 0.4 6554 6591 6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 -32 0007 .0007 .0006 0006 .0006 0006 .0006 0005 0005 .0006 0.5 6915 6950 .6985 7019 .7054 7088 .7123 7157 .7190 7224 -1.1 0010 .0009 .0009 0009 .0008 0008 .0008 0008 D007 .0007 -3.0 0013 .0013 .0013 0012 .0012 0011 0.6 7257 7291 7324 7357 7389 7422 .7454 .7486 .7517 7549 0011 .0011 0010 .0010 -29 0019 .0018 .0018 0017 .0016 0016 .0015 0015 0014 0014 0.7 7580 7611 7642 7673 7704 7734 7764 7794 .7823 7852 -2.8 0026 .0025 .0024 0023 .0023 .0022 .0021 0021 0020 .0019 0.8 .7881 7910 7939 7967 7995 8023 B051 8078 8106 8133 -2.7 0036 .0034 .0033 .0032 .0001 0030 .0029 0028 0027 0026 0.9 .8159 8186 8212 .8238 8264 8289 B315 8340 8365 8389 -2.6 0047 .0045 .0044 .0043 .0041 0040 .0039 0038 0037 .0036 1.0 .8413 8438 8461 8485 8508 .8531 B564 8577 8599 8621 -25 0062 .0060 .0069 0057 .0065 0064 .0052 0051 0049 .0048 1.1 8643 8665 8686 8708 8729 8749 8770 8790 8810 8830 .0089 -24 -2.3 0082 .0080 .0078 0075 .0073 0071 .0064 1.2 8849 8869 8888 8907 8925 8944 8962 8980 8997 9015 0107 .0104 .0102 0099 .0096 0094 .0091 0089 0087 .0084 1.3 9032 9049 9066 9082 9099 9115 9131 9147 .9162 9177 -22 0139 .0136 .0132 .0129 .0125 0122 .0119 0116 0113 0110 1.4 9192 9207 9222 9236 9251 9265 9279 9292 9306 9319 -2.1 0179 .0174 .0170 0166 .0162 0158 .0154 0150 0146 .0143 1.5 9332 .9345 .9357 9370 9382 9394 9406 9418 9429 9441 -2.0 0228 .0222 .0217 .0212 .0207 .0202 .0197 0192 0188 0183 1.6 9452 9463 .9474 9484 9495 9505 9515 9525 9535 9545 -1.9 0287 .0281 .0274 .0268 .0262 0256 .0250 0244 0229 .0233 1.7 .9554 9564 .9573 9582 .9591 9599 9608 9616 .9625 9633 -1.8 0359 .0361 .0344 0336 .0329 0322 .0314 .0301 .0294 -1.7 0446 .0436 .0427 .0418 .0409 0401 .0392 0384 0375 .0367 1.8 9641 9649 .9656 9664 9671 9678 9686 9693 9699 9706 -1.6 0548 .0537 0626 0516 .0505 0496 .0485 0475 0465 0455 1.9 9713 9719 9726 9732 9738 9744 9750 9756 9761 9767 -1.5 0688 .0666 .0843 0630 .0618 0606 .0594 0682 0671 0669 2.0 .9772 .9778 .9783 9788 9793 .9798 9803 9808 9812 9817 -1.4 0808 .0793 .0778 0764 .0749 .0735 .0721 0708 O694 0681 2.1 9821 9826 9830 9834 9838 9842 9846 9850 9854 9857 -13 0968 0951 0934 .0918 .0901 0885 .0889 0853 0838 0823 2.2 9861 9864 .9868 9871 9875 9878 9881 9884 9887 9890 -12 .1151 .1131 .1112 .1093 .1075 1056 1038 1020 1003 0985 2.3 .9893 .9896 .9898 9901 9904 9906 9909 9911 9913 9916 -1.1 .1357 1336 .1314 1292 .1271 .1251 .1230 1210 .1190 .1170 2.4 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 1446 1423 .1401 .1379 2.5 9938 9940 .9941 9943 9945 9946 9948 9949 9951 9952 -0.9 1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 2.6 9953 9955 .9956 9957 9959 9960 9961 9962 9963 9964 -0.8 2119 2090 2061 2033 2006 .1977 1949 1922 .1894 .1867 2.7 9965 9966 .9967 9968 9969 9970 9971 9972 9973 9974 -07 -0.6 2420 2389 2358 2327 .2296 2266 2236 2206 2177 .2148 2743 2709 2676 2643 .2611 2578 .2546 2514 2483 .2461 2.8 9974 .9975 .9976 9977 9977 9978 9979 9979 9980 .9981 9982 9982 9983 9988 -0.5 3086 3060 3015 2981 .2946 2912 2877 2843 2810 2776 2.9 9981 9984 9984 9985 9985 9986 9986 -04 3446 3409 .3372 3336 3300 3264 3228 3192 3156 .3121 3.0 9987 9987 9987 9988 9989 9989 9989 9990 9990 -03 3821 3703 .3745 3707 .3689 3632 3594 3567 3620 3483 3.1 9990 9991 .9991 9991 9992 9992 9992 9992 9993 9993 4207 4168 A129 A090 A052 4013 2974 2936 3897 3859 9995 9996 -02 3.2 9993 9993 9994 9994 9994 9994 9994 9995 9995 -01 4602 4662 A522 4483 A443 4404 4364 4325 A286 4247 9996 9997 3.3 9995 9995 9995 9996 9996 9996 9996 9997 -00 5000 4960 A920 4880 AB40 4801 .4761 4721 4681 4641 3.4 9997 9997 .9997 .9997 3997 9997 9997 .9997 9998 3.50 and up 00 .01 .02 02 04 05 06 07 08 09 9999 .00 .01 .02 .03 04 05 .06 .07 .08 09
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