Old Faithful The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with standard deviation 21.25 minutes, answer the following questions: Source: www. unmuseum. org

(a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? Round 4 decimals. (Hint: Use the standard deviation given to calculate the probability)

(b) Calculate and for the sampling distribution of the sample mean when the sample size is 20. (round 4 decimals if needed)

What is the probability that a random sample of 20 time intervals between eruptions has a mean longer than 95 minutes? Round 4 decimals.

(c) Calculate and for the sampling distribution of the sample mean when the sample size is 30. (round 4 decimals if needed) What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes? Round 4 decimals.

(d) What effect does increasing the sample size have on the probability? (increase, decrease, or stay the same) Why did this happen? In other word, what changed from part (a) to part (b) to part (c) in addition to or as a result of the sample size changing?

(e) Is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes unusual? (Refer to answer part (c)) Explain using complete sentences.

What might you conclude if a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes? (Hint: See conclusions for Example 5 on p. 375) Conclusion #1 Conclusion #2

(f) On a certain day, suppose there are 22 time intervals for Old Faithful. Treat these 22 eruptions as a random sample. Calculate and for the sampling distribution of the sample mean when the sample size is 22. (round 4 decimals if needed)

What length of time between eruptions must the time exceed if the probability is 0.20?