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 = 527 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 g? (Round your answer to four decimal places.)

(b)

What is the probability that the birth weight of a randomly selected full-term baby is between 3000 and 4000 g?(Round your answer to four decimal places.)

(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? (Round your answer to four decimal places.)

(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.)

Answer 1