7.72 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 m 5 3500 grams and standard deviation s 5 600 grams is a reasonable model for the probability distribution of the continuous numerical variable x 5 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? (Hint: 1 lb 5 453.59 g.)

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 Þ 0), then y 5 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?