Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a normal distribution with mean μ = 3500 grams and standard deviation σ = 647 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby.   (d) What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? (Hint: 1 lb = 453.59 g. Round your answer to four decimal places.)   (e) How would you characterize the most extreme 0.1% of all full-term baby birth weights? (Round your answers to the nearest whole number.) The most extreme 0.1% of birth weights consist of those greater than _____ grams and those less than _____ grams.   (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). (Round your answer to four decimal places.)

Question

Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a normal distribution with mean μ = 3500 grams and standard deviation σ = 647 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby.

 

(d) What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? (Hint: 1 lb = 453.59 g. Round your answer to four decimal places.)
 
(e) How would you characterize the most extreme 0.1% of all full-term baby birth weights? (Round your answers to the nearest whole number.)
The most extreme 0.1% of birth weights consist of those greater than _____ grams and those less than _____ grams.
 
(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). (Round your answer to four decimal places.)
 

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