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HW 3 Answer Key AEM 2100 1) z-score = (x-p)/o Male z-score = (75-69.9)/3 = 1.7 CI j' Female z-score = (70-64.6)/2.8 = 1.93 [r/ 1 The 70 inch woman is relatively taller because she has a higher z-score, which means compared to the population of women she is taller than the 75-inch man compared to the population of men. 2) a)x-bar = \$33.75 standard deviation = \$10 \$13.75 and \$53.75 are two standard deviations away from the mean. At least 75% of the prices of the meals will be between \$13.75 and \$53.75. G3 b) For any value z, at least 1-(l/z2) of the data values will lie within z standard deviations of the mean Z-score for \$50 (50-33.75)/10 = 1.625 3 1-(lI(1.625~)) = 62.1% 3 The largest proportion of meals that could be larger than \$50 is (100-62.1) = 37.9% 1 c) Mean price = \$33.75 x 8.0916 = 273.09 yen Standard Deviation = \$10 x 8.0916 = 80.92 yen J! 1 This will not change your answer from part a in terms of the z-scores. The only thing that will change is now at least 75% of the prices of the meals will now be between 111.26 yen (13.75 X 8.0916) and 434.92 yen (53.75 x 8.0916). (Answers may vary). Cj 1 b) Spain has the best environment since it has the lowest z-score. [ d] 3 a) 4) a) x-bar = 5309123 = 230.82 restaurants LGl Spain Guatemala Fiji **Should add the absolute values of the z scores for future reference. Ok if you didn't do it here. Procedures z-score (10-7.9)/2.9 = 0.724 (11-7.9)/2.9 = 1.07 (8-7.9)/2.9 = 0.034 Time z-score (47-27.9)/19.6 = 0.974 (26-27.9)/19.6 = -0.097 (46-27.9)/19.6 = 0.923 Cost z-score (15.1-14.2)/12.9 = 0.07 (47.3-14.2)/12.9 = 2.566 (25.3-14.2)/12.9 = 0.860 Combined z-score 1.768 3.733 or 3.539 1.817

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