Answer Happy

(i) List at least 3 anthropometric variables that you would need
to have to help the company choose a chair.
(ii) You decide that seat depth is a critical factor. The
university has a shortlist of 3 chairs but none of them has
adjustable seat depth. Seat depths are 450, 420 and 390 mm. Given
that the mean female buttock–popliteal length in is 457 mm (SD 33.6
mm), what percentage of the female workers will be able to sit on
the seats without having to adopt a posture, in which, they sit on
the edge of the seat?
(iii) Find the seat depth range which will accommodate 5 to 95
percentile of female population
For this question you need to use the statistical table provided
below.
Cumulative Standardized Normal Distribution A(z) is the integral of the standardized normal distribution from - co to z (in other words, the area under the curve to the left of z). It gives th probability of a normal random variable not being more than z standard deviations above its mean. Values of z of particular importance: A(z) 2 1.645 1.960 2.326 2.576 3.090 3.291 Az) 0.9500 0.9750 0.9900 0.9950 0.9990 0.9995 Lower limit of right 5% tail Lower limit of right 2.5% tail Lower limit of right 1% tail Lower limit of right 0.5% tail Lower limit of right 0.1% tail Lower limit of right 0.05% tail 3 3 -1 0 1 z 2 4 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.5000 0.5279 0.5359 0.5675 0.5753 0.5199 0.5596 0.5987 0.6368 0.6736 0.6985 0.7088 0.6064 0.6443 0.6808 0.7157 0.7486 7700 0.7794 0.8078 0.7422 0.7734 0052 0.8023 0.8289 0.8340 0.8531 0.0 0.1 0.2 03 0.4 0.5 0.6 07 0.7 0.8 no 0.9 10 1.0 11 1.1 13 1.2 13 1.3 14 1.4 15 1. 16 1.0 1.7 1.8 19 20 21 0.8577 8830 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 07001 0.7881 08150 0.8159 08413 0.8413 08643 0.8643 o8840 0.8849 00033 0.9032 00102 0.9192 0.9332 09 0 0452 0.9452 0.9554 0.9554 0.9641 0.9713 23 0.9772 2017 0.9821 204. 0.9801 0.9861 0.9893 0.9893 0.9918 0.9938 2000 09 0.9953 22 o 8888 0.5040 0.5080 0.5438 0.5478 0.5832 0.5871 0.6217 0.6255 0.6591 0.6628 0.6950 0.7291 7204 0.7324 eza 0.7611 0.7642 2010 4032 0.7910 0.7939 08186 0.8186 0891 0.8212 08438 0.8438 2461 0.8461 0 8665 0.8005 0.8686 08860 0.8869 0.8888 00040 0.9049 00066 0.9066 0.9207 00792 20 00345 6.9222 00357 27 00463 00474 0.9403 0.9474 0.9564 0.9573 0.9649 0.9049 0.9656 0.9719 0.9726 02 260 0.9778 0.9783 0.9826 2692 09020 0.9830 2004 0.9868 2000 0.9896 0.9898 0.9920 6.2003 0.9922 0040 0.9940 0045 9941 005 0.9955 2012 22 9956 0.9966 2000 .9967 3207 9976 9910 0.9982 0.9982 0.9987 0.9987 0.9991 0.9991 0.9993 0.9994 0.9995 0.9995 0.9997 0.9997 0.9998 0.9998 0.9998 0.9999 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 2672 0.7673 1067 0.7967 08938 0.8238 nes 0.8485 08708 0.8708 08007 0.8907 0089 0.9082 00236 0.9230 00370 0.9570 0 0484 0.9484 0 0582 0.9582 0.9664 0.9004 0.9732 09788 2600 0.9834 0.9837 0.9871 6.2011 0.9901 0.9925 0042 0.9943 0.9957 2015 6992 0.9968 0.9977 0.99!! 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 0.9998 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 07200 0.7704 -2005 0.7995 08764 0.8264 0.8508 08700 0.8729 08075 0.8925 0000 0.9099 09251 0.9231 00382 0.9382 0.9495 0.949 0.9591 0.9591 0.9671 0.9738 100 0.9793 232 0.9838 6.900 0.9875 0.9813 08700 0.8790 Sogo 0.8980 00147 0.9147 00002 00418 6.2494 0.9410 0.9525 0.952) 0.9616 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 1747 0.7764 oosi 0.8051 9215 0.8315 0.8554 08770 0.8770 0 8060 0.8902 00131 0.9131 00270 0.9219 0.9406 0.9400 0.9515 0.91 0.9608 0.9686 0.9750 0 9803 2012 0.9846 0.2010 0.9881 6.2001 0.9909 2007 0.9931 00040 0.9948 0.9961 24. 0.9971 0.9911 0.9979 26 0.9985 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9693 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 09106 0.8106 08365 0.8365 08500 0.8599 0.8810 o 2007 0.8997 00162 0.9102 00306 0930 0.9429 0.9429 00535 0.99 0.9625 0.902 0.9699 0.9761 2002 0.9812 20-2 0.9854 2007 0.9887 6.900 0.9913 6.2012 0.9934 00051 0.9951 02 0.9963 0022 22 0.9973 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9997 0.9998 08740 0.8749 08044 0.8944 00115 0.9115 0.9265 0.9202 00304 0.97 0.9505 0.930 0.9599 0.9399 0.9678 0.9744 0.9798 100 0.9842 2020 0:2012 0.9878 0.2010 0.9900 0.9906 0.9929 0.9946 00 0.9960 200 *10 0.9970 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9804 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 7050 0123 0.8133 0200 0.8389 8691 0.8621 0.8830 00015 0.9015 0.9177 00177 00310 00441 W.9319 0.9441 09545 0.9543 0.9033 0.9633 0.9706 0.9767 9102 09817 2017 0.9857 2001 0.9890 09890 0.9916 10 0.9936 0.9952 22 0.9964 07 0.9974 361 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9904 2.2 23 22 24 47 25 0.9756 20 0.9808 2040 0.9850 0.903 0.9884 0.9884 0.9911 0.9911 0.9932 *** 0.9962 0.9902 0.9972 0.2912 0.9949 0.9965 0.9974 0.9975 0.9978 0.9979 20 21 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 0.9981 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9927 001 0.9945 0.9959 20 0.9969 20 0.9977 0.9984 0.9988 0.9992 0.9994 0.9996 0.9997 0.9998 0.9985 9902 0.9989 0.9992 0.9995 0.9996 0.9997 0.9998