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?