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A parent was interested in the proportion of toddlers who go through the "mine" stage. This is identified as when a toddler refers to everything as "mine," even when it is not his or hers.

The parent randomly sampled $100$ other parents that went into toy store and asked them if their child has experienced the "mine" stage. Of these $100$ parents, $89$ parents said their child has gone through or is currently going through the "mine" stage.

Which of the following represents a $99.6\%$ confidence interval for the proportion of toddlers that go through the "mine" stage?

A

$0.89\pm 2.054\sqrt { \cfrac { (0.89)(0.11) }{ 100 } } $

B

$0.89\pm 2.652\sqrt { \cfrac { (0.89)(0.11) }{ 100 } } $

C

$0.89\pm 2.807\sqrt { \cfrac { (0.89)(0.11) }{ 100 } } $

D

$0.89\pm 2.878\sqrt { \cfrac { (0.89)(0.11) }{ 100 } } $

E

$0.89\pm 3.091\sqrt { \cfrac { (0.89)(0.11) }{ 100 } } $

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