# Question: showing work includes but is not limited to formulas graphs...

###### Question details

Showing work includes, but is not limited to: formulas, graphs and calculations. If you use the web calculator, StatCrunch, Minitab, Excel, Table V, etc… to find your probabilities, you must include your output with your answer

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. *(28 points)*

i) What is the probability that a random sample of 10 time intervals between eruptions has a mean time between 73 and 97 minutes?

ii) What is the probability that a random sample of 30 time intervals between eruptions has a mean time between 73 and 97 minutes?

Explain why the probabilities changed from part (i) to (ii). Be specific.