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Suppose a geyser has a mean time between eruptions of 75 minutes. Let the interval of...

Suppose a geyser has a mean time between eruptions of 75 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation
26 minutes. Complete parts ​(a) through ​(e) below

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

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

​(c) What is the probability that a random sample of 25 time intervals between eruptions has a mean longer than
87 ​minutes?

​(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 87 ​minutes, then the probability that the sample mean of the time between eruptions is greater than
87 minutes_______ because the variability in the sample mean ______ as the sample size ______

​(e) What might you conclude if a random sample of 25 time intervals between eruptions has a mean longer than
87 ​minutes? Select all that apply.

A.The population mean must be less than 75​, since the probability is so low.

B.The population mean is 75​, and this is an example of a typical sampling result.

C.The population mean cannot be 75​, since the probability is so low.

D.The population mean may be greater than 75.

E.The population mean is 75​, and this is just a rare sampling.

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