The school board claims that \[85\%\] of the over \[1{,}600\] families with children in their district send their children to public school. Skeptical of this claim, a private school administrator takes a simple random sample of \[120\] families with children in the district and asks them whether they send their children to public school. Assuming the school board's claim is correct, what is the probability that the administrator's results are within \[5\] percentage points of the school board's \[85\%\] claim? Choose 1 answer: Choose 1 answer: (Choice A) \[P(0.8<\hat p<0.9) \approx 0.73\] A \[P(0.8<\hat p<0.9) \approx 0.73\] (Choice B) \[P(0.8<\hat p<0.9) \approx 0.80\] B \[P(0.8<\hat p<0.9) \approx 0.80\] (Choice C) \[P(0.8<\hat p<0.9) \approx 0.87\] C \[P(0.8<\hat p<0.9) \approx 0.87\] (Choice D) \[P(0.8<\hat p<0.9) \approx 0.94\] D \[P(0.8<\hat p<0.9) \approx 0.94\]