Let X be the birth weight, in grams, of a randomly selected full-term baby. The article ““Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal
Body Composition” (Ultrasound Obstetrics Gynecol. 2009: 441–446) suggests that X is normally distributed with mean 3500 and standard deviation 600.
a. Sketch the relevant density curve, including tick marks on the horizontal scale.
b. What is P(3000 < X < 4500), and how does this compare to P(3000 ≤ X ≤ 4500)?
c. What is the probability that the weight of such a newborn is less than 2500 g?
d. What is the probability that the weight of such a newborn exceeds 6000 g (roughly 13.2 lb)?
e. How would you characterize the most extreme .1% of all birth weights?
f. Use the rescaling proposition from this section to determine the distribution of birth weight expressed in pounds (shape, mean, and standard deviation), and then
recalculate the probability from part (c).