Consider babies born in the \"normal\" range of 37–43 weeksgestational age. A paper suggests that a normal distribution withmean

μ = 3500 grams

and standard deviation

σ = 710 grams

is a reasonable model for the probability distribution of thecontinuous numerical variable

x = birth weight

of a randomly selected full-term baby.

(a)

What is the probability that the birth weight of a randomlyselected full-term baby exceeds 4000 g? (Round your answer to fourdecimal places.)

(b)

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

(c)

What is the probability that the birth weight of a randomlyselected full-term baby is either less than 2000 g or greater than5000 g? (Round your answer to four decimal places.)

(d)

What is the probability that the birth weight of a randomlyselected 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 allfull-term baby birth weights? (Round your answers to the nearestwhole number.)

The most extreme 0.1% of birth weights consist of those greaterthan  grams and those less than  grams.

(f)

If x is a random variable with a normal distributionand a is a numerical constant

(a ≠ 0),

then

y = ax

also has a normal distribution. Use this formula to determinethe distribution of full-term baby birth weight expressed in pounds(shape, mean, and standard deviation), and then recalculate theprobability from part (d). (Round your answer to four decimalplaces.)

How does this compare to your previous answer?

The value is much smaller than the probability calculated inpart (d).The value is about the same as the probability calculatedin part (d).    The value is much larger thanthe probability calculated in part (d).