Suppose a geyser has a mean time between eruptions of 74 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 26 minutes, answer the following questions.

(a) What is the probability that a randomly selected time interval between eruptions is longer than 85 minutes?

(b) What is the probability that a random sample of 10 time intervals between eruptions has a mean longer than 85 minutes?

(c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 85 minutes?

(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

(e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 85 minutes?

(f) On a certain day, suppose there are 22 time intervals for Old Faithful. Treating these 22 eruptions as a random sample, the likelihood the mean length of time between eruptions exceeds minutes is 0.20.