Question

Women in Belgium have a mean height of 168.1 centimeters with a standard deviation of 5.3 centimeters. Women in Turkey have a mean height of 156.4 centimeters with a standard deviation of 5.6 centimeters. a) Axelle Red is a famous Belgian singer who stands 165.1 centimeters. What is the Z-score for her height (please round to 2 decimal places)? b) Bengü Erden is a famous Turkish singer who stands 160.0 centimeters. What is the Z-score for her height (please round to 2 decimal places)? c) Which singer is taller in their respective group? O Axelle Red Bengü Erden d) What is the probability that a random Belgian woman is shorter than Axelle Red (please round to 4 decimal places)? e) What is the probability that a random Turkish woman is taller than Bengü Erden (please round to 4 decimal places)? e) What is the 80th percentile of heights of Turkish women (please round to 2 decimal places)?

Answer 1

For Belgium, Mean(u) 168.1 sed (o)= 5.3. we know, 7 score for X X-M 165.1 Height of Axella Red I-0.57 Z Score 165.1 168.1 5.3 b) 5.6 For Turkey, M = 156.4 Height of Bengiu Erden: 160.0 Z score 0.64 160-156.4 5.6 clearly Z score For Bengu Erden is. more than Axella. d) Here I Bengu Erden is taller in their respective Group. we want, P[ Z <-0157] ZNN(0) (-0.57) 0.2843 (From 7 table) we want, P[z> 0.64 $(-0.64) 0.2611 (From z table) let, soth percentile for turkish women M = 156.4,0 = 5.6 set, X: Height of Trakindor women. P[x<e] = o.so o >> S08 > Przec-M ] = & C 5" (08) : C-156.4 5.6 C- 156.4 506 Oo842 from z table table) > 156.4+ 5.64 0. 842 2 1161 12 soth percentile