Suppose a geyser has a mean time between eruptions of 60 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes.
Complete parts (a) through (e) below.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 70 minutes?
The probability that a randomly selected time interval is longer than 70 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 70 minutes?
The probability that the mean of a random sample of 12 time intervals is more than 70 minutes is approximately
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 27 time intervals between eruptions has a mean longer than 70 minutes?
The probability that the mean of a random sample of 27 time intervals is more than 70 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 70 minutes, then the probability that the sample mean of the time between eruptions is greater than 70 minutes
in the sample mean
as the sample size
because the variability