The most famous geyser in the world, Old Faithful in Yellowstone national park, has a mean time between eruptions of 85 minutes. Assume the interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. Define the random variable X to be the length of time between eruptions.

Use xbar to denote the distribution of the mean length of time between eruptions.

Question 1) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes?

a)State the probability statement with the random variable:

B)State the z-score, rounded to 2 decimal places:

c)State the answer, rounded to 4 decimal places:

Question 2) Suppose we take a random sample of the 20-time interval between eruptions.

a)State the mean of the distribution of the sample mean:

b) State the standard deviation of the distribution of the sample mean, rounded to 2 decimal places.

Question 3) What is the probability that a random sample of 20-time intervals between eruptions has a mean longer than 95 minutes?

a)Give the probability statement with the random variable:

b)State the z-score, rounded to 2 decimal places:

c) Give the answer, rounded to 4 decimal places

Question 4 ) Suppose we take a random sample of 30 time interval between eruptions.

a)State the mean of the distribution of the sample mean:

b)State the standard deviation of the distribution of the sample mean, rounded to 2 decimal places

Question 5) What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 95 minutes?

a)Give the probability statement with the random variable:

b)State the z-score, rounded to 2 decimal places:

c) Give the answer, rounded to 4 decimal places:

Question 6) What effect does increasing the sample size have on the probability?

Question 7) What might you conclude if a random sample of 30-time intervals between eruptions has a mean longer than 95 minutes?

Question 8) On a certain day, suppose there are 22-time intervals for Old Faithful. Treating these 22 eruptions as a random sample, complete the following sentence:

a)The likelihood the mean length of time between eruptions exceeds _____________ minutes is 0.20.

b)Give answer rounded to 2 decimal places.