91Ó°ÊÓ

The scores on a college entrance exam have an approximate normal distribution with mean, $Â\mu =52$ points and a standard deviation, $\mathrm{σ}=11$ points.

From empirical rule it is known that $68\%$will have $-1$and $1z$-scores. And, the values will be:

$x_1=\mathrm{μ}+z\mathrm{σ}$

$=52+1×11$

$=63$

And,

$x_1=\mathrm{μ}+z\mathrm{σ}$

$=52-1×11$

localid="1648294753461" $=41$

Therefore, the $68\%$values will fall between $\mathbf{41}$and$\mathbf{63}$.

The scores on a college entrance exam have an approximate normal distribution with mean,$Â\mu =52$ points and a standard deviation, $\mathrm{σ}=11$ points.

From empirical rule it is known that $95\%$will have $-2$and $2z$-scores. And, the values will be:

$x_1=\mathrm{μ}+z\mathrm{σ}$

localid="1648296180774" $=52+2×11$

$=74$

$x_1=\mathrm{μ}+z\mathrm{σ}$

$=52-2×11$

$30$

Therefore, the $95\%$values will fall between $\mathbf{30}$and $\mathbf{74}$.

The scores on a college entrance exam have an approximately normal distribution with mean, $Â\mu =52$points and a standard deviation, $\mathrm{σ}=11$ points.

From empirical rule it is known that $99.7\%$ will have $-3$ and $3$-scores. And, the values will be:

$x_1=\mathrm{μ}+z\mathrm{σ}$

$=52+3×11$

$=85$

And

$x_1=\mathrm{μ}+z\mathrm{σ}$

$=52-3×11$

$=19$

Therefore, the $99.7\%$values will fall between $19$and $85$.