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Having a cholesterol level above $200\text{ mg/dL}$ is a definite cause for concern. Do women have more reason to be concerned than men?

On average, men's cholesterol level is $191\text{ mg/dL}$ with a standard deviation of $46\text{ mg/dL}$. For women, the average is $196\text{ mg/dL}$ with a standard deviation of $44\text{ mg/dL}$.

A computer randomly selects the medical records of $30\text{ men}$ and $30\text{ women}$ and calculates the difference of the average cholesterol level of the two genders. This process is repeated many times.

What is the standard deviation of the sampling distribution of the difference of the mean cholesterol levels for men and women?

A

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { { 46 }^{ 2 }+{ 44 }^{ 2 } }$

B

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \dfrac { 46 }{ 30 } +\dfrac { 44 }{ 30 } }$

C

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \dfrac { { 46 }^{ 2 } }{ 30 } +\dfrac { { 44 }^{ 2 } }{ 30 } }$

D

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\dfrac { \sqrt { { 46 }^{ 2 }+{ 44 }^{ 2 } } }{ 30 }$

E

${ \sigma }_{ { \overline { x } }_{ M }-{ \overline { x } }_{ W } }=\sqrt { \dfrac { { 46 }^{ 2 } }{ 30 } } +\sqrt { \dfrac { { 44 }^{ 2 } }{ 30 } }$

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