Suppose a geyser has a mean time between eruptions of 76 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. (round everything to four decimal places)
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 14 time intervals between eruptions has a mean longer than 87 minutes?
c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 87 minutes?
d) What effect does increasing the sample size have on the probability? Fill in the blanks with either increases or decreases.
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 26 time intervals between eruptions has a mean longer than 87 minutes? Choose the best answer.
A) The population mean must be more than 76, since the probability is so low.
B) The population mean is 76, and this is an example of a typical sampling result.
C) The population mean must be less than 76, since the probability is so low.
D) The population mean may be greater than 76.