Question

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 = 3432 g and standard deviation o = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes. Compute the z-score of an infant who weighs 4230 g. (Round your answer to two decimal places.) Approximately what fraction of infants would you expect to have birth weights between 2340 g and 4160 g? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of infants would you expect to have birth weights below 2340 g? (Express your answer as a decimal, not a percent, and round to three decimal places.) A medical researcher wishes to study infants with low birth weights and seeks infants with birth weights among the lowest 5%. Below what weight must an infant's birth weight be in order for the infant be included in the study? (Round your answer to the nearest gram.) 34,707 29

Answer 1

482 Am let X, denote birth weights of infant whose mothers did not have a history of diabetes. Then Xm N(M= 3432,0=482). * The 2-score of an infant who eighs x=4230 g is Z2 X 4 = 4230-3432 = 1.66 The fraction of infants would have birth weights between ed 2340 g and 4160 g is given by P( 2340 2 X 24160) - Pl 2340-3432 << 4160-3433.) 482 = P(-2.2656<2<15104) = (1.5104) - 5 (-2.2656) = $(1.5104) + (2.2656)-) = 0.935+0.988-1=0.923 * The fraction of infants would have birth weights below 23409 is given by P 142 34 00- 2022 2346-34 32 ) = P(Z<-2.2656) 482 = (-2.2656) = |- ( 2.2656) - |- 0.988 = 0.012 An infant be in the study if it belongs to the lowest 5% of infanty birth weights. That is P(XX) = 0,05 =) 1=0.05 B ( ada = 0.05= 0 (-1,645) 1-14--1645 = X5 3432-1.645x 482 26399 so an infant's birth weight must be 2639 g in order that infant be included in the studly. plass