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 $\mu = 78$.

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 $\mu = 78$ and $\sigma = 6$:
$\mu - 2\sigma=78-2\times6 = 78 - 12=66$
$\mu + 2\sigma=78 + 2\times6=78 + 12 = 90$
Since $66<84<90$, 84 is within 2 standard deviations of the mean.

Answer:

It is within 2 standard deviations of the mean.