Question

according to a medical journal, the distribution of weights of newborn babies is approximately normal, with a mean of 3390 grams and a standard deviation of 550 grams. use a technology or a table to answer parts (a) through (c) below. for each include an appropriately labeled and shaded normal curve. the percentage of newborn babies that weigh between 3100 and 3900 grams is 52.6%. (round to one decimal place as needed.) c. a baby is classified as \low birth weight\ if the baby weighs less than 2400 grams at birth. what percentage of newborns would we expect to be \low birth weight\? select the correct graph below.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 2400\), \(\mu=3390\), and \(\sigma = 550\).

$$z=\frac{2400 - 3390}{550}=\frac{-990}{550}=- 1.8$$

Step2: Find the cumulative probability

Using a standard normal table or technology (e.g., TI - 84: normalcdf\((-\infty,-1.8)\) or Excel: NORM.S.DIST\((-1.8,TRUE)\)), we find the cumulative probability for \(z=-1.8\).
The cumulative probability \(P(Z < - 1.8)\) is approximately \(0.0359\) or \(3.6\%\)

For the graph:
We are interested in the area to the left of \(x = 2400\) (since we want the percentage of babies with weight less than \(2400\) grams).

• Option A is wrong because it shades the area to the right of the mean.
• Option C is wrong because it shades the area to the right of \(x = 2400\) (but we want \(x<2400\)).
• Option D is wrong because it shades the area around the mean.
• Option B is correct as it shades the area to the left of \(x = 2400\)

Answer:

The percentage of newborns classified as "low birth weight" is \(3.6\%\). The correct graph is B.