Suppose a geyser has a mean time between eruptions of T! minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 2'." minutes. Complete parts (a) through (e) below. [a] What is the probability that a randomly selected time interval between eruptions is longer than 83 minutes? The probability that a randomly selected time interval is longer than 83 minutes is approximately (Round to four decimal plaoes as needed.) [b] What is the probability that a random sample of 15 time intervals between eruptions has a mean longer than 33 minutes? The probability that the mean of a random sample of '15 time intervals is more than 83 minutes is approximately (Round to four decimal plaoes as needed.) [c] What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 88 minutes? The probability that the mean of a random sample of 29 time intervals is more than 83 minutes is approximately (Round to four decimal plaoes as needed.) [cl] What effect does increasing the sample size have on the probabilit Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 38 minutes. then the probability that the sample mean of the time between eruptions is greater than 33 minutes Y because the variability in the sample mean V as the sample size Y [e] What might you oonolude if a random sample of 29 time intervals between eruptions has a mean longer than 38 minutes? Select all that apply. The population mean is 77, and this is an example of a typical sampling result. The population mean may be less than 77. The population mean must be less than N. sinoe the probability is so low. The population mean is 77, and this is just a rare sampling. The population mean may be greater than 77. Insane? The population mean cannot be Ta", since the probability is so low