The data set has mean $10$ and standard deviation$3$ . Fill in the following blanks:
a. Approximately $68\%$ of the observations lie between_ and _
b. Approximately$95\%$ of the observations lie between_ and _
c. Approximately$99.7\%$ of the observations lie between _and _

We are given data set has mean $10$ and standard deviation$3$.

Here we will use Empirical Rule, according to it , approximately , $68\%$ of observations are within $1$standard deviation of mean .

So we will use formula $\mu -\sigma =10-7=3$, here $\mu$is mean which is $10$ and $\sigma =3$which is standard deviation .

Similarly , localid="1650873767168" role="math" $\mu +\sigma =10+3=13$

So answer is that it is between$3$and$13$

We are given that data set has mean $10$ and standard deviation$3$ .

Here we will use Empirical Rule, according to it , approximately , $95\%$ of observations are within$2$standard deviation of mean .

So we will use formula , localid="1650873598136" $\mu -2\sigma =10-6=4$, here$\mu$ is mean which is$10$ and localid="1650873635986" $\sigma =3$which is standard deviation .

Similarly , localid="1650873684206" $\mu +2\sigma =10+6=16$

So answer is that it is between$4$ and localid="1650873740762" $16$

We are given that data set has mean $10$and standard deviation$3$ .

Here we will use Empirical Rule, according to it , approximately ,$99.7\%$ of observations are within$3$standard deviation of mean .

So we will use formula , localid="1650873826689" $\mu -3\sigma =10-9=1$, here $\mu$is mean which is$\sigma$ and which is standard deviation .

Similarly ,localid="1650873848324" $\mu +3\sigma =10+9=19$

So answer is that it is between localid="1650873858373" $1$and$19$