A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 55 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? ^ The table entry for z is the area to the left of z. TABLE 5 Areas of a Standard Normal Distribution (a) Table of Areas to the Left of z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0003 .0003 .0003 .0005 0005 0005 .0007 .0007 .0006 0006 0005 .0005 -3.1 .0010 -3.0 .0013 .0013 .0003 .0003 .0003 .0003 .0003 .0003 .0002 0004 .0004 0004 .0004 .0004 0004 .0003 0006 0006 .0006 0005 0009 .0009 .0009 .0008 0008 .0008 0008 0007 .0007 0013 0012 0012 0011 0011 0011 0010 0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 0033 0032 0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 0044 0043 .0041 .0040 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 0082 .0080 .0078 0075 .0073 0071 .0069 0068 0066.0064 -2.3 .0107 0104 .0102 .0099 .0096 0094 .0091 .0089 .0087 .0084 -2.2 0139 .0136 .0132 .0129 .0125 .0122 .0119 -2.1 .0179 .0174 0170 .0166 .0162 0158 0154 0150 .0146 0143 -2.0 .0228 0222 0217 0212 .0207 .0202 .0197 0192 0188 0183 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 0233 -1.8 .0359 .0351 .0344 .0336 .0329 0322 0314 .0307 0301 .0294 -1.7 0446 .0436 0427 0418 .0409 0401 0392 .0384 0375 .0367 -1.6 .0548 0537 .0526 .0516 .0505 0495 0485 .0475 -1.5 .0668 0655 0643 0630 .0618 0116 0113 0110 0465 .0455 0606 .0594 .0582 0571 .0559 0694 .0681 0838 .0823 1003 0985 -1.4 0808 0793 0778 0764 0749 0735 0721 0708 -1.3 .0968 .0951 .0934 0918 0901 .0885 .0869 0853 -1.2 1151 1131 .1112 .1093 -1.1 .1357 1335 .1314 1292 -1.0 .1587 .1562 .1539 .1515 -0.9 .1841 .1814 .1788 .1762 1075 1056 1038 1020 1271 1251 1230 1210 1190 1170 .1492 1469 .1446 .1423 1401 .1379 1736 1711 .1685 1660 1635 .1611 Z -3.4 -3.3 -3.2
A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 55 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? ^ The table entry for z is the area to the left of z. TABLE 5 Areas of a Standard Normal Distribution (a) Table of Areas to the Left of z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0003 .0003 .0003 .0005 0005 0005 .0007 .0007 .0006 0006 0005 .0005 -3.1 .0010 -3.0 .0013 .0013 .0003 .0003 .0003 .0003 .0003 .0003 .0002 0004 .0004 0004 .0004 .0004 0004 .0003 0006 0006 .0006 0005 0009 .0009 .0009 .0008 0008 .0008 0008 0007 .0007 0013 0012 0012 0011 0011 0011 0010 0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 0033 0032 0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 0044 0043 .0041 .0040 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 0082 .0080 .0078 0075 .0073 0071 .0069 0068 0066.0064 -2.3 .0107 0104 .0102 .0099 .0096 0094 .0091 .0089 .0087 .0084 -2.2 0139 .0136 .0132 .0129 .0125 .0122 .0119 -2.1 .0179 .0174 0170 .0166 .0162 0158 0154 0150 .0146 0143 -2.0 .0228 0222 0217 0212 .0207 .0202 .0197 0192 0188 0183 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 0233 -1.8 .0359 .0351 .0344 .0336 .0329 0322 0314 .0307 0301 .0294 -1.7 0446 .0436 0427 0418 .0409 0401 0392 .0384 0375 .0367 -1.6 .0548 0537 .0526 .0516 .0505 0495 0485 .0475 -1.5 .0668 0655 0643 0630 .0618 0116 0113 0110 0465 .0455 0606 .0594 .0582 0571 .0559 0694 .0681 0838 .0823 1003 0985 -1.4 0808 0793 0778 0764 0749 0735 0721 0708 -1.3 .0968 .0951 .0934 0918 0901 .0885 .0869 0853 -1.2 1151 1131 .1112 .1093 -1.1 .1357 1335 .1314 1292 -1.0 .1587 .1562 .1539 .1515 -0.9 .1841 .1814 .1788 .1762 1075 1056 1038 1020 1271 1251 1230 1210 1190 1170 .1492 1469 .1446 .1423 1401 .1379 1736 1711 .1685 1660 1635 .1611 Z -3.4 -3.3 -3.2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is
normally distributed, with a mean of 55 months and a standard deviation of 9 months. If the company does not want to make refunds for more than
10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Z
0
The table entry for z is the area to
the left of z.
TABLE 5 Areas of a Standard Normal Distribution
(a) Table of Areas to the Left of z
.09
Z
-3.4
.00 .01 .02 .03
.0003 .0003 .0003
.0005 .0005 .0005
-3.3
-3.2
.0005 .0005
-3.1
.0007 .0007
.0010 .0010
.04
.05 .06 .07 .08
.0003
.0003 .0003 .0003 .0003 .0003 .0002
.0004 .0004 .0004 .0004 .0004 .0004 .0003
.0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005
.0010 .0009 .0009 .0009 .0008 .0008 0008 .0008
-3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011
-2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
-2.8
.0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
-2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
-2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
-2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
-2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
-2.3 .0107 0104 .0102 .0099
.0096
.0094 .0091 .0089 .0087 .0084
-2.2 .0139 .0136 .0132 .0129
.0125
-2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
-2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
-1.9 .0287 .0281 .0274 0268
.0262 .0256 .0250 .0244 .0239 .0233
-1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
-1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
-1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
-1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
-1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681
-1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823
-1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985
-1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170
-1.0 .1587 .1562 .1539 .1515 .1492 .1469
-0.9 .1841 .1814 .1788 .1762 .1736 .1711
.0122 .0119 .0116 .0113 .0110
.1446 .1423 .1401 .1379
.1685 .1660 .1635 .1611
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