Question

1. men’s heights the distribution of heights of adult american men is approximately normal with mean 69 inches and standard deviation 2.5 inches. draw an accurate sketch of the distribution of men’s heights. be sure to label the mean, as well as the points 1, 2, and 3 standard deviations away from the mean on the horizontal axis.

Explanation:

Step1: Recall normal - distribution properties

A normal distribution is bell - shaped.

Step2: Calculate values for standard deviations

Mean $\mu = 69$, standard deviation $\sigma=2.5$.
1 - std dev: $69\pm2.5$ (i.e., $66.5$ and $71.5$).
2 - std dev: $69\pm2\times2.5$ (i.e., $64$ and $74$).
3 - std dev: $69\pm3\times2.5$ (i.e., $61.5$ and $76.5$).

Step3: Sketch the distribution

Draw a bell - shaped curve. Label the mean at the center ($x = 69$). Mark $66.5,71.5$ for 1 std dev, $64,74$ for 2 std dev, and $61.5,76.5$ for 3 std dev on the horizontal axis.

Answer:

Sketch a normal curve with mean 69 and marked points for 1, 2, 3 std devs as calculated above.