# Question

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?

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?

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