Suppose a geyser has a mean time between eruptions of 85minutes. If the interval of time between the eruptions is normally distributed with standard deviation 34minutes, answer the following questions.

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(a) What is the probability that a randomly selected time interval between eruptions is longer than 100 minutes?

The probability that a randomly selected time interval is longer than 100 minutes is approximately

nothing

. (Round to four decimal places asneeded.)

(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 100 minutes?

The probability that the mean of a random sample of 13 time intervals is more than 100 minutes is approximately

nothing

. (Round to four decimal places asneeded.)

(c) What is the probability that a random sample of 27 time intervals between eruptions has a mean longer than 100 minutes?

The probability that the mean of a random sample of 27 time intervals is more than 100 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. Choose the correct answer below.

A.

The probability increases because the variability in the sample mean decreases as the sample size increases.

B.

The probability increases because the variability in the sample mean increases as the sample size increases.

C.

The probability decreases because the variability in the sample mean decreases as the sample size increases.

D.

The probability decreases because the variability in the sample mean increases as the sample size increases.

(e) What might you conclude if a random sample of 27 time intervals between eruptions has a mean longer than 100 minutes? Choose the best answer below.

A.

Thepopulationmeanmustbemorethan85,sincetheprobabilityissolow.

B.

Thepopulationmeancannotbe85,sincetheprobabilityissolow.

C.

The population mean is 85 minutes, and this is an example of a typical sampling.

D.

Thepopulationmeanmaybegreaterthan85.

Click to select your answer(s).