Question

19. 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 u = 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. a) (5pts) Approximately what fraction of infants would you expect to have birth weights between 2780 g and 3780 g? b) (2pts) A medical researcher wishes to study infants with low birth weights and seeks infants with birth weights among the lowest 16%. 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.)

Answer 1

Consider X be a random variable which follows normal distribution indicates the birth weight of infants. The mean is 3432 g with a standard deviation of 482 g. a) The fraction of infants that are expected to have birth weights between 2780 g and 3780 g is, 2780 - 3432 x-u 3780-3432 P(2780 < X <3780) = P 482 482 = P(-1.3527 < z<0.7219) = P(z<0.7219) - P(z<-1.3527) (using 2-table) = 0.7648 -0.0881 = 0.6767 b) The required birth weight is, P(X Sa) = 0.16 2-3432 = 0.16 482 a-3432 0 (0.16) (Using z-table) 482 - 3432 = -0.9945 482 a = 3432+(-0.9945x 482) = 2952.651 2953 g a-