Question
Asked Jul 5, 2019
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In a population of ages where the mean age is 45 and the standard deviation is 5.25, what are the ages of the youngest 5% and the oldest 5%. Round your solutions to the nearest tenth.

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Expert Answer

Step 1

Given mean age = 45
Standard deviation = 5.25
The Z score with 0.0505 to its left is -1.64 and the Z score with 0.0495 to its left is -1.65. So we can say on average the Z score with 0.05 to its left is -1.645.

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0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.0016 0.0014 -2.9 0,0019 0,0018 0,0018 0.0017 0,0016 0.0015 0.0015 0.0014 0.0024 0,0023 0.0021 0.0021 0.0020 -2.8 0.0026 0.0025 0.0023 0.0022 0.0019 0.0029 0.0026 -2.7 0.0035 0,0034 0.0033 0,0032 0,0031 0,0030 0.0028 0.0027 0.0045 0.0039 0.0038 0.0036 -2.6 0.0047 0.0044 0.0043 0.0041 0.0040 0.0037 0.0049 0.0048 -2.5 0,0062 0.0060 0.0059 0,0057 0.0055 0.0054 0,0052 0,0051 0.0082 0.0080 0.0068 0.0064 -2.4 0.0078 0.0075 0.0073 0.0071 0.0069 0.0066 -2.3 0.0107 0.0104 0.0102 0,0099 0,0096 0.0094 0.0091 0.0089 0.0087 0.0084 0.0119 0.0116 0.0110 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0113 0.0158 0.0146 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0154 0.0150 0.0143 0.0212 0.0183 -2.0 0.0228 0.0222 0.0217 0.0207 0.0202 0.0197 0.0192 0.0188 0.0262 0.0250 0.0233 -1.9 0.0287 0.0281 0.0274 0.0268 0.0256 0.0244 0.0239 0.0344 0.0301 0.0294 -1.8 0.0359 0.0351 0.0336 0.0329 0.0322 0.0314 0.0307 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 0.0505 -1.6 0.0548 0.0537 0.0526 0.0516 0.0495 0.0485 0.0475 0.0465 0.0455

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Step 2

Using the formula of Z score and by substituting the values we get the age of youngest 5% is 36.4 (rounded to tenth place).

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Χ. Z-μ σ X -45 -1.645 5.25 X-45 8.63625 X 36.36375

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Step 3

The Z score with 0.0505 to its right is 1.64 and the Z score with 0.0495 to its right is...

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0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.4681 0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4641 0.4562 0.1 0.4602 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.4168 0.3936 0.3897 0.3859 0.2 0.4207 0.4129 0.4090 0.4052 0.4013 0.3974 0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 0.3192 0.3121 0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3156 0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.1949 0.1867 0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1922 0.1894 0.1788 0.1635 0.9 0.1841 0.1814 0.1762 0.1736 0.1711 0.1685 0.1660 0.1611 0.1401 0.1379 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1230 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1210 0.1190 0.1170 0.1112 0.1075 0.1003 0.0985 1.2 0.1151 0.1131 0.1093 0.1056 0.1038 0.1020 1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 0.0808 0.0793 0.0681 1.4 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0606 1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0594 0.0582 0.0571 0.0559 0.0495 1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0485 0.0475 0.0465 0.0455

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