Suppose a geyser has a mean time between eruptions of 69 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 81 minutes? The probability that a randomly selected time interval is longer than 81 minutes is approximately (Round to four decimal places as needed.) (b) What is the probability that a random sample of 12 time intervals between eruptions has a mean longer than 81 minutes? The probability that the mean of a random sample of 12 time intervals is more than 81 minutes is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 81 minutes? The probability that the mean of a random sample of 26 time intervals is more than 81 minutes is approximately (Round to four decimal places as needed.)

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Suppose a geyser has a mean time between eruptions of 69 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. 

(e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 81 minutes? Select all that apply.
O A. The population mean must be less than 69, since the probability is so low.
B. The population mean cannot be 69, since the probability is so low.
C. The population mean is 69, and this is an example of a typical sampling result.
D. The population mean is 69, and this is just a rare sampling.
] E. The population mean may be greater than 69.
] F. The population mean may be less than 69.
O G. The population mean must be more than 69, since the probability is so low.
Transcribed Image Text:(e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 81 minutes? Select all that apply. O A. The population mean must be less than 69, since the probability is so low. B. The population mean cannot be 69, since the probability is so low. C. The population mean is 69, and this is an example of a typical sampling result. D. The population mean is 69, and this is just a rare sampling. ] E. The population mean may be greater than 69. ] F. The population mean may be less than 69. O G. The population mean must be more than 69, since the probability is so low.
Suppose a geyser has a mean time between eruptions of 69 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. Complete
parts (a) through (e) below.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 81 minutes?
The probability that a randomly selected time interval is longer than 81 minutes is approximately
(Round to four decimal places as needed.)
(b) What is the probability that a random sample of 12 time intervals between eruptions has a mean longer than 81 minutes?
The probability that the mean of a random sample of 12 time intervals is more than 81 minutes is approximately
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 81 minutes?
The probability that the mean of a random sample of 26 time intervals is more than 81 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 81 minutes, then the probability that the sample mean of the time between eruptions is greater than 81 minutes
V because the variability in
the sample mean
as the sample size
Transcribed Image Text:Suppose a geyser has a mean time between eruptions of 69 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 81 minutes? The probability that a randomly selected time interval is longer than 81 minutes is approximately (Round to four decimal places as needed.) (b) What is the probability that a random sample of 12 time intervals between eruptions has a mean longer than 81 minutes? The probability that the mean of a random sample of 12 time intervals is more than 81 minutes is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 81 minutes? The probability that the mean of a random sample of 26 time intervals is more than 81 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 81 minutes, then the probability that the sample mean of the time between eruptions is greater than 81 minutes V because the variability in the sample mean as the sample size
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