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.

Explanation:

Step1: Recall the properties of the normal distribution

The normal distribution is symmetric about the mean. We are interested in the probability that \(x>3900\). The mean \(\mu = 3390\) and the standard deviation \(\sigma=550\). The region \(x > 3900\) is to the right of the mean.

Step2: Analyze each graph

• Graph A: The shaded region is to the left of \(3900\), which is not what we want (we want \(P(X>3900)\)).
• Graph B: The shaded regions are on both sides of the mean, not relevant for \(P(X > 3900)\).
• Graph C: The shaded region is to the right of \(3900\), which is the region we are interested in for calculating \(P(X>3900)\).
• Graph D: The shaded region is to the left of \(3900\) (mostly, since the peak is at the mean \(3390\) and the shaded area is left - skewed relative to \(3900\) in terms of the probability we need).

Answer:

C.