A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 23 minutes, with a standard deviation of 3.7 minutes. Assume the distribution of trip times to be normally distributed. Complete parts (a) through (e) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) What is the probability that a trip will take at least hour? (Round to four decimal places as needed.) (b) If the office opens at 9:00 A.M. and the lawyer leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work? %☐ (Round to two decimal places as needed.) (c) If he leaves the house at 8:35 AM. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee? (Round to four decimal places as needed.) (d) Find the length of time above which we find the slowest 15% of trips. ☐ minutes (Round to three decimal places as needed.) (e) Find the probability that 2 of the next 3 trips will take at least hour. (Round to four decimal places as needed.)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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I need help with this please parts d and e 

A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 23 minutes, with a standard deviation of 3.7 minutes. Assume the distribution of trip times to be normally distributed. Complete parts (a) through (e) below.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
1
2
(a) What is the probability that a trip will take at least hour?
(Round to four decimal places as needed.)
(b) If the office opens at 9:00 A.M. and the lawyer leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
% ☐
(Round to two decimal places as needed.)
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(Round to four decimal places as needed.)
(d) Find the length of time above which we find the slowest 15% of trips.
minutes
(Round to three decimal places as needed.)
(e) Find the probability that 2 of the next 3 trips will take at least
hour.
2
(Round to four decimal places as needed.)
Transcribed Image Text:A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 23 minutes, with a standard deviation of 3.7 minutes. Assume the distribution of trip times to be normally distributed. Complete parts (a) through (e) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 1 2 (a) What is the probability that a trip will take at least hour? (Round to four decimal places as needed.) (b) If the office opens at 9:00 A.M. and the lawyer leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work? % ☐ (Round to two decimal places as needed.) (c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee? (Round to four decimal places as needed.) (d) Find the length of time above which we find the slowest 15% of trips. minutes (Round to three decimal places as needed.) (e) Find the probability that 2 of the next 3 trips will take at least hour. 2 (Round to four decimal places as needed.)
Areas under the Normal Curve
Area
#
-3.4
.00
.03
0.0003
.04
0.0003
-1.7 0.0446 0.0436
0.0427
田
2
.00
.01
.02
.03
.04
.01
.02
.05
.06
0.0003 0.0003 0.0003
0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004
-3.2 0.0007 0.0007 0.0006
0.0006 0.0006 0.0006 0.0006 0.0005
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021
-2.7 0.0035 0.0034 0.0033 0.0032
0.0031 0.0030 0.0029
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069
0.0066 0.0064 -2.4
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091
0.0087 0.0084 -2.3
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119
0.0113 0.0110 -2.2
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162
0.0158 0.0154 0.0150 0.0146 0.0143 -2.1
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197
0.0192 0.0188 0.0183 -2.0
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250
0.0244 0.0239 0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020
0.1003 0.0985 -1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423
0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6
-0.5 0.3085 0.3050 0.3015 0.2981
0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974
0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.07
.08
.09
.07
.08
.09
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.0014 0.0014 -2.9
0.0021 0.0020 0.0019 -2.8
0.0028 0.0027 0.0026 -2.7
0.0038 0.0037 0.0036 -2.6
0.0051
0.0068
0.0089
0.0116
0.0049 0.0048 -2.5
1
.05
.06
2
固
Areas under the Normal Curve
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675
0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.1
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726
0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0,9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
0.9884 0.9887 0.9890 2.2
0.9901 0.9904 0.9906 0,9909 0.9911 0.9913 0.9916 2.3
0.9932 0.9934 0.9936 2.4
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881
2.3 0.9893 0,9896 0.9898
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
0.9990 3.0
田
2.9
+ V
3.0
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
A 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.02
.03
2
.00
.01
.04
.05
.06
.07
.08
.09
Transcribed Image Text:Areas under the Normal Curve Area # -3.4 .00 .03 0.0003 .04 0.0003 -1.7 0.0446 0.0436 0.0427 田 2 .00 .01 .02 .03 .04 .01 .02 .05 .06 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0066 0.0064 -2.4 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0087 0.0084 -2.3 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0113 0.0110 -2.2 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.2 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 .07 .08 .09 .07 .08 .09 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 0.0007 0.0007 -3.1 0.0010 0.0010 -3.0 0.0014 0.0014 -2.9 0.0021 0.0020 0.0019 -2.8 0.0028 0.0027 0.0026 -2.7 0.0038 0.0037 0.0036 -2.6 0.0051 0.0068 0.0089 0.0116 0.0049 0.0048 -2.5 1 .05 .06 2 固 Areas under the Normal Curve .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0.9772 0.9778 0,9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9890 2.2 0.9901 0.9904 0.9906 0,9909 0.9911 0.9913 0.9916 2.3 0.9932 0.9934 0.9936 2.4 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 2.3 0.9893 0,9896 0.9898 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 0.9990 3.0 田 2.9 + V 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 A 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .02 .03 2 .00 .01 .04 .05 .06 .07 .08 .09
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