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Sampling distributions

A high school newspaper claims that 15%15\% of all students experienced extreme levels of stress during the past month. Skeptical about this claim, you decide to take a simple random sample of 8080 of the 10001000 students at the school, and ask them if they experienced extreme levels of stress during the past month. Subsequently, you find that 20%20\% of the sample replied “yes” to your question.
Assuming that the newspaper’s 15%15\% claim is correct, what is the approximate probability that 20%20\% or more of 8080 randomly selected students from this school would report that they experienced extreme levels of stress during the past month?
Round your answer to the nearest hundredth.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}