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# Suppose a geyser has a mean time between eruptions of 79 minutes

- From Mathematics, Probability

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Suppose a geyser has a mean time between eruptions of 79 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts **(a)** through **(e)** below.

The probability that a randomly selected time interval is longer than 89 minutes is approximately ____. (Round to four decimal places as needed.)

**(b)** What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 89 minutes?

The probability that the mean of a random sample of 13 time intervals is more than 89 minutes is approximately ____. (Round to four decimal places as needed.)

**(c)** What is the probability that a random sample of 24 time intervals between eruptions has a mean longer than 89 minutes?

The probability that the mean of a random sample of 24 time intervals is more than 89 minutes is approximately _____. (Round to four decimal places as needed.)

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

If the population mean is less than 89 minutes, then the probability that the sample mean of the time between eruptions is greater than 89 minutes _____▼ (Increase -or- decrease) because the variability in the sample mean _____▼(Increase -or- decrease) as the sample size _____▼ (decreases / increases).

**(e)** What might you conclude if a random sample of 24 time intervals between eruptions has a mean longer than 89 minutes? Select all that apply.

A.The population mean must be more than 79, since the probability is so low.

B.The population mean may be less than 79.

C.The population mean must be less than 79, since the probability is so low.

D.The population mean is 79, and this is an example of a typical sampling result.

E.The population mean is 79, and this is just a rare sampling.

F.The population mean may be greater than 79.

G. The population mean cannot be 79, since the probability is so low.

## [Solved] Suppose a geyser has a mean time between eruptions of 79 minutes

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- Submitted On 17 Jun, 2020 04:58:16

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