Question

standard deviation of 3.2
does the number line below correctly
display three standard deviations away
from the mean?
yes, it is correctly displayed.
no. there is a mistake on the left side of the mean.
no. there is a mistake on the left and right side of the mean.
no. you start with the median, not the mean.

Explanation:

Step1: Calculate values for left side

The mean is \(20\) and standard deviation \(\sigma = 3.2\).
For one - standard deviation below the mean: \(20-3.2=16.8\)
For two - standard deviations below the mean: \(20 - 2\times3.2=20 - 6.4 = 13.6\)
For three - standard deviations below the mean: \(20-3\times3.2=20 - 9.6=10.4\)
But on the left - hand side of the mean (\(20\)) in the number line, the values are \(20.4\), \(23.6\), \(26.8\) which are greater than the mean.

Step2: Analyze the right - hand side

For one - standard deviation above the mean: \(20 + 3.2=23.2\)
For two - standard deviations above the mean: \(20+2\times3.2=20 + 6.4 = 26.4\)
For three - standard deviations above the mean: \(20+3\times3.2=20 + 9.6 = 29.6\)
The values on the right - hand side of the mean (\(20\)) in the number line: \(23.2\), \(25.4\), \(28.6\). The value \(25.4\) is not a multiple of the standard deviation from the mean (\(20+3.2 = 23.2\), \(20 + 2\times3.2=26.4\)).

Answer:

No. There is a mistake on the left and right side of the Mean.