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?