Question

the graph shows a distribution of data with a standard deviation of 6
which statement is true about the data point 84?
it is within 1 standard deviation of the mean.
it is within 2 standard deviations of the mean
it is exactly 3 standard deviations from the mean.
it is exactly 4 standard deviations from the mean

Explanation:

Step1: Find the mean

From the graph, the mean $\mu = 75$.

Step2: Calculate the range within 2 standard deviations

The standard deviation $\sigma=6$.
The range within 2 standard deviations of the mean is $\mu - 2\sigma$ to $\mu + 2\sigma$.
Substitute $\mu = 75$ and $\sigma = 6$:
$\mu - 2\sigma=75-2\times6=75 - 12 = 63$
$\mu + 2\sigma=75+2\times6=75 + 12 = 87$

Since $63<84<87$, the data point 84 is within 2 standard deviations of the mean.

Answer:

It is within 2 standard deviations of the mean.