Suppose a geyser has a mean time between eruptions of 97minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 25minutes. Complete parts (a) through (e) below.

(a) What is the probability that a randomly selected time interval between eruptions is longer than 109 minutes?

The probability that a randomly selected time interval is longer than 109 minutes is approximately

nothing

.

(Round to four decimal places asneeded.)

(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 109 minutes?

The probability that the mean of a random sample of 8 time intervals is more than 109 minutes is approximately

nothing

.

(Round to four decimal places asneeded.)

(c) What is the probability that a random sample of 28 time intervals between eruptions has a mean longer than 109 minutes?

The probability that the mean of a random sample of 28 time intervals is more than 109 minutes is approximately

nothing

.

(Round to four decimal places asneeded.)

(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 109 minutes, then the probability that the sample mean of the time between eruptions is greater than 109 minutes

increases

decreases

because the variability in the sample mean

decreases

increases

as the sample size

increases.

decreases.

(e) What might you conclude if a random sample of 28 time intervals between eruptions has a mean longer than 109 minutes? Select all that apply.

A.

The population mean is 97, and this is an example of a typical sampling result.

B.

The population mean cannot be 97, since the probability is so low.

C.

The population mean must be less than 97, since the probability is so low.

D.

The population mean may be greater than 97.

E.

The population mean may be less than 97.

F.

The population mean is 97, and this is just a rare sampling.

G.

The population mean must be more than 97, since the probability is so low.