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

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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.

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