Question

suppose the birth weights of full - term babies are normally distributed with mean 3300 grams and standard deviation \\( \sigma=490 \\) grams. complete parts (a) through (c) below.
(a) draw a normal curve with the parameters labeled. choose the correct graph below.
(b) shade the region that represents the proportion of full - term babies who weigh more than 4280 grams. choose the correct graph below.
(c) suppose the area under the normal curve to the right of \\( x = 4280 \\) is 0.0228. provide an interpretation of this result. select the correct choice below and fill in the answer box to complete your
choice.
(type a whole number.)
a. the probability is 0.0228 that the birth weight of a randomly chosen full - term baby in this population is less than \\( \square \\) grams.
b. the probability is 0.0228 that the birth weight of a randomly chosen full - term baby in this population is more than \\( \square \\) grams.

Explanation:

• For part (a), a normal curve with mean \( \mu = 3300 \) grams and standard deviation \( \sigma=490 \) grams should have the center at \( x = 3300 \).
• For part (b), since we want the region representing the proportion of full - term babies who weigh more than \( 4280 \) grams, we shade the area to the right of \( x = 4280 \).
• For part (c), the area under the normal curve to the right of \( X = 4280 \) being \( 0.0228 \) means that the probability that a randomly - chosen full - term baby in this population is more than \( 4280 \) grams is \( 0.0228 \).

Answer:

(a) The correct graph is the one with the center at \( x = 3300 \).
(b) Shade the area to the right of \( x = 4280 \) on the normal curve.
(c) A. The probability is \( 0.0228 \) that the birth weight of a randomly chosen full - term baby in this population is more than \( 4280 \) grams.