A geyser has a mean time between eruptions of 86 minutes.
If the interval of time between the eruptions is normally distributed with standard deviation 19 minutes, answer the following questions. (5 Parts total a-e)
(a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? The probability that a randomly selected time interval is longer than 95 minutes is approximately _____________?.(Round to four decimal places as needed.)
(b) What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 99 time intervals is more than 9595 minutes is approximately _______________? (Round to four decimal places as needed.)
(c) What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 29 time intervals is more than 95 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. Choose the correct answer below.
A. The probability increases because the variability in the sample mean decreases as the sample size increases.
B. The probability decreases because the variability in the sample mean decreases as the sample size increases.
C. The probability increases because the variability in the sample mean increases as the sample size increases.
D. The probability decreases because the variability in the sample mean increases as the sample size increases.
(e) What might you conclude if a random sample of 29 time intervals between eruptions has a mean longer than 95minutes? Choose the best answer below.
A. The population mean must be less than 86, since the probability is so low.
B. The population mean cannot be 86, since the probability is so low.
C. The population mean may be greater than 86.
D. The population mean is 86 minutes, and this is an example of a typical sampling.