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.
a. what is the probability that a newborn baby will weigh more than 3900 grams? select the correct graph below.
the probability that a newborn baby will weigh more than 3900 grams is %
(round to one decimal place as needed)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 3900\), \(\mu=3390\), and \(\sigma = 550\).

$$z=\frac{3900 - 3390}{550}=\frac{510}{550}\approx0.93$$

Step2: Find the probability using the standard normal table

We want \(P(X>3900)\), which is equivalent to \(P(Z > 0.93)\).
Since \(P(Z>z)=1 - P(Z\leq z)\), and from the standard - normal table \(P(Z\leq0.93)=0.8238\)

$$P(Z > 0.93)=1 - 0.8238=0.1762$$

Step3: Convert to percentage

To convert the probability to a percentage, we multiply by \(100\).

$$0.1762\times100 = 17.62\approx17.6$$

Answer:

\(17.6\)