Question

create a graph of the normal distribution with a mean ($mu$) of 2.2 and a standard deviation ($sigma$) of 0.8. show your work here draw $mu = 0$ $sigma = 1$ toggle empirical rule reset

Explanation:

Step1: Identify key - points

The mean $\mu = 2.2$ is the center of the normal distribution. The standard deviation $\sigma=0.8$.

Step2: Mark the mean on the x - axis

On the x - axis of the graph, mark the point $x = 2.2$ which will be the peak of the bell - shaped curve.

Step3: Determine intervals

Calculate the intervals $\mu\pm\sigma,\mu\pm2\sigma,\mu\pm3\sigma$.
$\mu-\sigma=2.2 - 0.8=1.4$, $\mu+\sigma=2.2 + 0.8 = 3.0$;
$\mu-2\sigma=2.2-2\times0.8=2.2 - 1.6 = 0.6$, $\mu + 2\sigma=2.2+2\times0.8=2.2 + 1.6 = 3.8$;
$\mu-3\sigma=2.2-3\times0.8=2.2 - 2.4=-0.2$, $\mu + 3\sigma=2.2+3\times0.8=2.2 + 2.4 = 4.6$.

Step4: Sketch the curve

Sketch a smooth, symmetric bell - shaped curve centered at $x = 2.2$ with inflection points at $x=\mu\pm\sigma$ (i.e., $x = 1.4$ and $x = 3.0$). The curve approaches the x - axis but never touches it.

Answer:

A normal distribution graph centered at $x = 2.2$ with inflection points at $x = 1.4$ and $x = 3.0$, and the curve approaching the x - axis as $x$ moves away from the mean in both directions.