Question

the graph shows a distribution of data. what is the variance of the data? 0.0625 0.25 0.5 1.5

Explanation:

Step1: Recall empirical rule for normal distribution

For a normal - distribution, approximately 68% of the data lies within 1 standard - deviation ($\sigma$) of the mean. In the given normal - distribution graph, the interval that contains about 68% of the data is from 3.5 to 4.5. The mean ($\mu$) is at 4.
The formula for the range of the 68% confidence interval is $\mu-\sigma$ to $\mu + \sigma$. So, if $\mu-\sigma=3.5$ and $\mu = 4$, then $4-\sigma=3.5$, which gives $\sigma = 0.5$.

Step2: Calculate the variance

The variance ($\sigma^{2}$) is related to the standard - deviation ($\sigma$) by the formula $\sigma^{2}=\sigma\times\sigma$. Since $\sigma = 0.5$, then $\sigma^{2}=(0.5)\times(0.5)=0.25$.

Answer:

0.25