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3. [10] A triangular distribution which approximates womens height in inches is given by: 0.0064x - 0.32 for 50<x< 62.5 f(x)-(-0.0064 + 48 for 62.5 x Prove that this expression is a pdf. 4. [51 Using the distribution provided in problem 3, find the proportion of women with a height between 60 and 65 inches.
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Answer #1

4)P(60 <X <65)=62.5 60 (0.0064x-0.32) dx +int_{62.5}^{65} (-0.0064x+0.48) dx

=(0.0064x2/2-0.32x)|62.560 +(-0.0064*x2/2+0.48x)|6562.5 =0.18+0.18 =0.36

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