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Many methods have been developed to try to accurately predict a child's eventual adult height from various factors. One simple method to predict adult height is to average theparents' heights in inches and then add 2.5 inches if the child is a boy or subtract 2.5 inches if the child is a girl. This method can be fairly accurate, but can also be as much as 5 inches above or below the child's eventual height. Write a formula or formulas to express this calculation, and clearly define any variables that you use.

Another method is to add the parents' heights in inches and then add an additional 5 inches if the child is a boy or subtract 5 inches if the child is a girl. This total is then divided by 2 to predict the child's ultimate height. Write a formula or formulas for this method, using variables you've already defined. How do these formulas compare to the first onesdescribed? Are they equivalent? Show how they are equivalent or explain why they are not.

A third method, referred to as the "mid-parent rule," uses a weighted average of the parents' heights in inches in which the height of the opposite-gender parent is multiplied by a factor of before it is averaged with the other parent's height. Write a formula to express this calculation. Is it equivalent to the first two formulas? Explain fully.

These early, simple methods gave pediatricians and parents quick ways to estimate a child's adult height, but they are not terribly accurate. A new statistical model was eventually developed based on age, weight, and parental height data from a large, longitudinal study. This method, called the Khamis-Roche method, can be applied only to healthy Caucasian children over the age of 4. To use this method, coefficients must be obtained from a table, multiplied by the corresponding measurement, and then added together with the constant to generate a formula to predict a child's height. The partial tables that follow give the coefficients for girls aged 4 to 7. Write a formula for this method to predict the height of a 5-year-old girl, clearly defining any variables you use.

GIRLS	AGE	Constant Term	Coefficient of Current Height (in.)	Coefficient of Current Weight (lb)	Coefficient of Average Parental Height(in.)
	4	-8.13250	1.24768	-0.019435	0.44774
	5	-5.13582	1.19932	-0.017530	0.38467
	6	-3.51039	1.15866	-0.015400	0.34105
	7	-2.87645	1.11342	-0.013184	0.31748

BOYS	AGE	Constant Term	Coefficient of Current Height (in.)	Coefficient of Current Weight (lb)	Coefficient of Average Parental Height(in.)
	4	-10.2567	1.23812	-0.0087235	0.50286
	5	-11.0213	1.10674	-0.0064778	0.53919
	6	-11.1138	1.05923	-0.0052947	0.52513
	7	-10.9984	1.05877	-0.0048144	0.48538

Use all four methods described to predict the ultimate adult height of a 5-year-old girl if her current height is 3' 6'' and her weight is 43 pounds. Assume her mother is 5'5'' and her father is 6'1'' tall. Then use all four methods again to predict the height for you or someone you know. Which of these methods would have most accurately predicted theheight?

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