Question

The data set has mean$15$and standard deviation $2$. Approximately what percentage of the observations lie between $13$and $17$?

Short answer

The percentage of the observations lie between $13$and $17$is$68\%$

Step-by-step solution

Step 1:Given information

We are given that data set has mean$15$and standard deviation$2$ .

Simplify

We will use empirical rule, to determine approximate values for the percentage of observations between$13$and$17$.

We are given that $\mu =15$and$\sigma =2$, where $\mu$is mean and $\sigma$is standard deviation.

Also , the given interval $(13,17)$will be formed by adding and subtracting standard deviations from the mean.We will check for different values of $k$.

So using the value of mean and standard deviation , we get , $\left(\mu -k\sigma ,\mu +k\sigma \right)=(13,17)\Rightarrow k=1$

By empirical rule , $P\left(\mu -\sigma <X<\mu +\sigma \right)\approx 0.68$where $X$is given interval.

So percentage is$68\%$