9. The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. The interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. What is the probability that a randomly selected time interval between eruptions is longer than 60 minutes? What is the probability that a random sample of 20 time-intervals has a mean longer than 60 minutes? What is the probability that a random sample of 30 time-intervals has a mean between 80 and 84 minutes? What is the bottom 5% of time-intervals between eruptions?

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