91Ó°ÊÓ

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 $\mathrm{μ}-\mathrm{σ}=10-7=3$, here $\mathrm{μ}$is mean which is $10$ and $\mathrm{σ}=3$which is standard deviation .

Similarly , localid="1650873767168" role="math" $\mathrm{μ}+\mathrm{σ}=10+3=13$

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" $\mathrm{μ}-2\mathrm{σ}=10-6=4$, here$\mathrm{μ}$ is mean which is$10$ and localid="1650873635986" $\mathrm{σ}=3$which is standard deviation .

Similarly , localid="1650873684206" $\mathrm{μ}+2\mathrm{σ}=10+6=16$

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" $\mathrm{μ}-3\mathrm{σ}=10-9=1$, here $\mathrm{μ}$is mean which is$\mathrm{σ}$ and which is standard deviation .

Similarly ,localid="1650873848324" $\mathrm{μ}+3\mathrm{σ}=10+9=19$

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