Consider babies born in the “normal” range of 37–43 weeks gestational age. The paper referenced in Example 7.13 (“Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal Body Compo- sition,” Ultrasound in Obstetrics and Gynecology [2009]: 441–446) suggests that a normal distribution with mean m = 3500 grams and standard deviation s 5 600 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby.
a. What is the probability that the birth weight of a randomly selected full-term baby exceeds 4000 grams? Is between 3000 and 4000 grams?
b. What is the probability that the birth weight of a randomly selected full-term baby is either less than 2000 grams or greater than 5000 grams?
c. What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? (1 pound = 453.59 grams)
d. How would you characterize the most extreme 0.1% of all full-term baby birth weights?
e. If x is a 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 (c). How does this compare to your previous answer?