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Sampling Distribution of Sample Prop: Get Off Social Media, Mom!

APSTAT-JMMX4I

A recent survey in the town of Pleasantville found that $55\%$ of the adults had a social media account. The true percentage of adults that have a social media account in Pleasantville is $58\%$.

Using simple random samples of size $100$, what are the mean and standard deviation respectively, for the sampling distribution of the sample proportions of adults who own a social media account in Pleasantville?

A

$0.55,\quad \sqrt { 100(0.55)(0.45) } $

B

$0.55,\quad \sqrt { \cfrac { (0.55)(0.45) }{ 100 } } $

C

$0.58,\quad \sqrt { 100(0.58)(0.42) } $

D

$0.58,\quad \sqrt { \cfrac { (0.55)(0.45) }{ 100 } } $

E

$0.58,\quad \sqrt { \cfrac { (0.58)(0.42) }{ 100 } } $