Question

in the united states, birth weights of newborn babies are approximately normally distributed with a mean of \\(\mu = 3,500\text{ g}\\) and a standard deviation of \\(\sigma = 500\text{ g}\\).

what percent of babies born in the united states are classified as having a low birth weight (< 2,500 g)? explain how you got your answer.

Explanation:

Identify given parameters

Using the Normal Distribution knowledge point

$$ \mu = 3500\text{ g},\quad \sigma = 500\text{ g},\quad X < 2500\text{ g} $$

Calculate the z-score

Using the Z-Score Formula knowledge point

$$ z = \frac{X - \mu}{\sigma} = \frac{2500 - 3500}{500} = -2 $$

Apply the empirical rule

Using the Empirical Rule knowledge point

$$
LATEXBLOCK0
$$

Answer:

\(2.5\%\)