Question

the graph shows a distribution of data. what is the standard deviation of the data? 0.5 1.5 2.0 2.5

Explanation:

Step1: Recall normal - distribution property

In a normal distribution, about 68% of the data lies within one standard - deviation of the mean. The mean of this normal distribution is $\mu = 2$. The interval within one standard - deviation of the mean is from $\mu-\sigma$ to $\mu + \sigma$.

Step2: Identify the interval

The interval from 1.5 to 2.5 seems to represent the interval within one standard - deviation of the mean. If $\mu = 2$ and the lower bound of the interval is $\mu-\sigma=1.5$ and the upper bound is $\mu+\sigma = 2.5$.

Step3: Solve for $\sigma$

If $\mu-\sigma=1.5$ and $\mu = 2$, then $2-\sigma=1.5$, so $\sigma=0.5$. Also, if $\mu+\sigma=2.5$ and $\mu = 2$, then $2+\sigma=2.5$, so $\sigma = 0.5$.

Answer:

0.5