Suppose a geyser has a mean time between eruptions of 65 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 15 minutes.
Complete parts (a) through (e) below.
I ONLY NEED HELP ON THE QUESTION PART (E) I SELECTED B,F,G BUT it stated that one or more of my answers was wrong? Please help?
(a) What is the probability that a randomly selected time interval between eruptions is longer than 72 minutes?
The probability that a randomly selected time interval is longer than 72 minutes is approx. 0.3192
(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 72 minutes.
The probability that the mean of a random sample of 13 ttime intervals is more than 72 minutes is approximately 0.0465.
(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 72 minutes?
The probability that the mean of a random sample of 26 time intervals is more than 72 minutes is approximately 0.0087
(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 72 minutes, then the probability that the sample mean of the time between eruptions is greater than 72 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 72 minutes? Select all that apply.
A.The population mean is 65, and this is an example of a typical sampling result.
B.The population mean cannot be 65, since the probability is so low.
C.The population mean may be greater than 65.
D.The population mean is 65, and this is just a rare sampling.
E.The population mean must be more than 65, since the probability is so low.
F.The population mean may be less than 65.
G.The population mean must be less than 65, since the probability is so low.
I ONLY NEED HELP ON THE QUESTION PART (E) I SELECTED B,F,G BUT it stated that one or more of my answers was wrong? Please help?
Correct option is C:
C.The population mean may be greater than 65.
(since there is a possibility even small the population mean is 65 ,therefore we can not reject that population mean is 65. But this gives strong indication that population mean may be greater than 65. )
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