Math Problem Statement
Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?" The American Statistician, Nov 1999, 53:4). However, they also found that when infants born outside of the "typical" 37-43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean μ = 3432 g and standard deviation σ = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes. Approximately what fraction of infants would you expect to have birth weights above 3340 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Probability
Z-Score
Formulas
z = (x - μ) / σ
P(X > x) = 1 - P(Z ≤ z)
Theorems
Properties of the Normal Distribution
Standard Normal Distribution
Suitable Grade Level
Grades 10-12
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