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 = 710 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.)

How does this compare to your previous answer?

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

Answer 1

mean

μ = 3500 grams

and standard deviation

σ = 710 grams

a)

b)

c)

d)  probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds

given 1lb =453.59

7lb =3175.13

.

*** Dear student we answer four sub parts once post remaining separately****