Question

draw a normal curve with a mean of 63 and a standard deviation of 16. describe how you constructed the curve and discuss its features. choose the correct graph of the normal curve below. describe how you constructed the curve and discuss its features. the normal distribution curve is centered at (square) and has 2 points of inflection, (square) representing (mu-sigma), and (square) representing (mu + sigma). (type integers or decimals.)

Explanation:

Step1: Recall properties of normal curve

The normal curve is symmetric about the mean $\mu$. Given $\mu = 63$ and $\sigma=16$.

Step2: Calculate values for inflection - points

The inflection - points of a normal curve are at $\mu-\sigma$ and $\mu + \sigma$.
$\mu-\sigma=63 - 16=47$
$\mu+\sigma=63 + 16=79$
The normal curve is centered at the mean. So it is centered at 63.

Step3: Analyze the graphs

We are looking for a graph centered at 63 with inflection - points at 47 and 79. Graph A has values 47, 63, 79 which match our calculations for the center and inflection - points.

Answer:

A.
The normal distribution curve is centered at 63 and has 2 points of inflection, 47 representing $\mu-\sigma$, and 79 representing $\mu+\sigma$.