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Sampling Distribution of a Sample Mean: Roll that Dice

APSTAT-XN1LP8

The roll of a six-sided die has a uniform distribution with a mean outcome of $3.5$ and a standard deviation of approximately $1.708$.

Which of the following best describes the sampling distribution of the sample means when the same dice is rolled $48$ times?

A

Uniform with a ${ \mu }_{ \overline { x } }=3.5\quad and\quad a\quad \sigma _{ \overline { x } }=1.708$

B

Uniform with a ${ \mu }_{ \overline { x } }=3.5\quad and\quad a\quad \sigma _{ \overline { x } }=\cfrac { 1.708 }{ \sqrt { 48 } } $

C

Normal with a ${ \mu }_{ \overline { x } }=3.5\quad and\quad a\quad \sigma _{ \overline { x } }=\cfrac { 1.708 }{ \sqrt { 48 } } $

D

Approximately normal with a ${ \mu }_{ \overline { x } }=3.5\quad and\quad a\quad \sigma _{ \overline { x } }=1.708$

E

Approximately normal with a ${ \mu }_{ \overline { x } }=3.5\quad and\quad a\quad \sigma _{ \overline { x } }=\cfrac { 1.708 }{ \sqrt { 48 } } $