Suppose a geyser has a mean time between eruptions of63minutes. Let the interval of time between the eruptions be normally distributed with standard deviation18minutes. Complete parts (a) through (e) below.

(a)What is the probability that a randomly selected time interval between eruptions is longer than72 minutes?

The probability that a randomly selected time interval is longer than 72 minutes is approximately______

(b) What is the probability that a random sample of8 time intervals between eruptions has a mean longer than72 minutes?

The probability that the mean of a random sample of 8 time intervals is more than 72 minutes is approximately ______

(c) What is the probability that a random sample of19 time intervals between eruptions has a mean longer than72 minutes?

The probability that the mean of a random sample of

19 time intervals is more than 72 minutes is approximately

(d)What effect does increasing the sample size have on theprobability? Provide an explanation for this result. Fill in the blanks below.

If the population mean is less than 72 minutes, then the probability that the sample mean of the time between eruptions is greater than 72 minutes ____ because the variability in the sample mean_____as the sample size _____

(e) What might you conclude if a random sample of19 time intervals between eruptions has a mean longer than72 minutes? Select all that apply.

A. The population mean must be less than 63, since the probability is so low.

B. The population mean must be more than 63, since the probability is so low

C. The population mean is 63, and this is just a rare sampling.

D. The population mean may be less than 63

E. The population mean is 63, and this is an example of a typical sampling result

F. The population mean cannot be 63, since the probability is so low

G. The population mean may be greater than 63