Question: In recent years there has been considerable discussion about the appropriateness of the body shapes and proportions of the Ken and Barbie dolls. These dolls are very popular, and there is some concern that the dolls may be viewed as having the "ideal body shape," potentially leading young children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes scaled Ken and Barbie up to a common height of 170.18 cm (5'7") and compared them to body measurements of active adults. Common measures of body shape are the chest (bust), waist, and hip circumferences. These measurements for Ken and Barbie and their reference groups are presented in the table below:

Doll and Human Reference Group Measurements (cm)

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1. Convert Ken's chest, waist, and hips measurements to z-scores. Which of those measures appears to be the most different from Ken's reference group? Justify your response with an appropriate statistical argument. (10 points)
2. The z-scores for Barbie's Chest, Waist, and Hips when compared to active female adults are approximately -1.4, -6.2, and -4.7, respectively. Do these z-scores provide evidence to justify the claim that the Barbie doll is a thin representation of adult women? Justify your response with an appropriate statistical argument. (5 points)
3. If men's waist measurements are approximately normally distributed, based on the sample above what is the approximate percentile of a 100 cm waist? (8 points)

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