Suppose a geyser has a mean time between eruptions of 65 min. Let the interval of time between the eruptions be normally distributed with standard deviation 19 min. Complete parts (a) through (e) below.

a. What is the probability that a randomly selected time interval between eruptions is longer than 73 min.?

b. What is the probability that a random sample of 15 time intervals between eruptions has a mean longer than 73 min.?

c. What is the probability that a random sample of 33 time intervals between eruptions has a mean longer than 73 min?

d. What effect does increasing the sample size have on the probability? Provide an explanation for this result.

e. What might you conclude if a random sample of 33 time intervals between eruptions has a mean longer than 73 minutes? Select all that apply.

__ The population mean may be greater than 65.

__ The population mean is 65, and this is just a rare sampling

__ The population mean must be less than 65, since the probability is so low

__ The population mean may be less than 65

__ The population mean must be more than 65, since the probability is so low

__ The population mean is 65, and this is an example of a typical sampling result

__ The population mean cannot be 65, since the probability is so low