Consider babies born in the "normal" range of 37-43 weeks gestational age. The paper referenced in Example 7.27 ("Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal Body Composition," Ultrasound in Obstetrics and Gynecology [2009]: 441-446) suggests that a normal distribution with mean µ = 3500 grams and standard deviation a = 600 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected fullterm baby.
a. What is the probability that the birth weight of a randomly selected full-term baby exceeds 4000 g?
b. What is the probability that the birth weight of a randomly selected full-term baby is between 3000 and 4000 g?
c. What is the probability that the birth weight of a randomly selected full-term baby is either less than 2000 g or greater than 5000 g?
d. What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? e. How would you characterize the most extreme 0.1% of all full-term baby birth weights?
f. If x is a random variable with a normal distribution and a is a numerical constant (a ≠ 0), then y = ax also has a normal distribution. Use this formula to determine the distribution of full-term baby birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from Part (d). How does this compare to your previous answer?